929:
1723:
1813:
826:
666:
transversely. For nondegenerate
Hamiltonian diffeomorphisms, one variant of the Arnold conjecture says that the number of fixed points is at least equal to the minimal number of critical points of a
1997:
1339:
1297:
251:
1411:
330:
124:
1512:
464:
1579:
964:
838:
634:
750:
1607:
1258:
1226:
491:
1906:
1868:
1125:
602:
84:
1174:
664:
402:
1086:
1057:
1012:
144:
1543:
1449:
368:
174:
1148:
1599:
1473:
1359:
1194:
1032:
712:
688:
562:
542:
515:
422:
274:
194:
2334:
2301:
2195:
2070:
2023:
Rizell, Georgios
Dimitroglou; Golovko, Roman (2017-01-05). "The number of Hamiltonian fixed points on symplectically aspherical manifolds".
2284:
Oh, Yong-Geun (1995), "Floer cohomology of
Lagrangian intersections and pseudo-holomorphic disks, III: Arnold-Givental Conjecture",
2221:
Givental, A. B. (1989b), "Periodic maps in symplectic topology (translation from Funkts. Anal. Prilozh. 23, No. 4, 37-52 (1989))",
1744:
755:
2329:
2324:
1940:
1909:
1968:
1515:
1302:
1263:
202:
147:
1367:
286:
93:
983:
1478:
430:
924:{\displaystyle \#\{{\text{fixed points of }}\varphi \}\geq \sum _{i=0}^{2n}\dim H_{i}(M;{\mathbb {F} })}
43:
1828:
Lazzarini proved it for negative monotone case under suitable assumptions on the minimal Maslov number.
1873:
2319:
2260:
1718:{\displaystyle \#(\varphi _{1}(L)\cap L)\geq \sum _{i=0}^{n}\dim H_{i}(L;\mathbb {Z} /2\mathbb {Z} )}
1548:
1452:
937:
607:
277:
731:
1935:
726:
87:
39:
1231:
1199:
469:
2238:
2154:
2024:
2000:
1879:
1841:
1098:
979:
575:
57:
1153:
643:
373:
2297:
2191:
2066:
1925:
2261:"Floer cohomology and Arnol'd-Givental's conjecture of [on] Lagrangian intersections"
129:
2289:
2246:
2230:
2164:
2058:
718:
2276:
2178:
1521:
1416:
335:
152:
2272:
2250:
2174:
2054:
425:
35:
17:
1130:
1066:
1037:
992:
1930:
1912:
1584:
1458:
1344:
1179:
1017:
697:
673:
667:
547:
527:
500:
407:
259:
179:
2145:
Frauenfelder, Urs (2004), "The Arnold–Givental conjecture and moment Floer homology",
1821:
proved it for real forms of compact
Hermitian spaces with suitable assumptions on the
2313:
2242:
1831:
1822:
1818:
722:
544:
is greater than or equal to the number of critical points of a smooth function on
2293:
2048:
2169:
2205:
1835:
1965:
Asselle, L.; Izydorek, M.; Starostka, M. (2022). "The Arnold conjecture in
1734:
The Arnold–Givental conjecture has been proved for several special cases.
524:
states that the number of fixed points of a
Hamiltonian diffeomorphism of
1738:
370:. This family induces a 1-parameter family of Hamiltonian vector fields
2234:
283:
Suppose there is a smooth 1-parameter family of
Hamiltonian functions
2159:
2062:
424:. The family of vector fields integrates to a 1-parameter family of
2029:
2005:
982:, gives a lower bound on the number of intersection points of two
2186:
Fukaya, Kenji; Oh, Yong-Geun; Ohta, Hiroshi; Ono, Kaoru (2009),
1475:. This family generates a 1-parameter family of diffeomorphisms
2188:
Lagrangian intersection Floer theory - anomaly and obstruction
604:
be a closed symplectic manifold. A Hamiltonian diffeomorphism
1228:
be an anti-symplectic involution, that is, a diffeomorphism
1808:{\displaystyle (M,L)=(\mathbb {CP} ^{n},\mathbb {RP} ^{n})}
721:, the Morse number is greater than or equal to the sum of
821:{\textstyle \sum _{i=0}^{2n}\dim H_{i}(M;{\mathbb {F} })}
758:
1971:
1882:
1844:
1747:
1610:
1587:
1551:
1524:
1481:
1461:
1419:
1370:
1347:
1305:
1266:
1234:
1202:
1182:
1156:
1133:
1101:
1069:
1040:
1020:
995:
940:
841:
734:
700:
676:
646:
610:
578:
550:
530:
503:
472:
433:
410:
376:
338:
289:
262:
205:
182:
155:
132:
96:
60:
1991:
1900:
1862:
1807:
1717:
1593:
1573:
1537:
1506:
1467:
1443:
1405:
1353:
1333:
1291:
1252:
1220:
1188:
1168:
1142:
1119:
1080:
1051:
1026:
1006:
958:
923:
820:
744:
706:
682:
658:
628:
596:
556:
536:
509:
485:
458:
416:
396:
362:
324:
268:
245:
188:
168:
138:
118:
78:
1545:. The Arnold–Givental conjecture states that if
2128:
38:, is a mathematical conjecture in the field of
2084:
2082:
8:
2089:
1992:{\displaystyle \mathbb {C} \mathbb {P} ^{n}}
966:a nondegenerate Hamiltonian diffeomorphism.
856:
845:
2147:International Mathematics Research Notices
2265:Comptes Rendus de l'Académie des Sciences
2168:
2158:
2102:
2028:
2004:
1983:
1979:
1978:
1973:
1972:
1970:
1908:is a certain symplectic reduction, using
1881:
1843:
1796:
1792:
1789:
1788:
1778:
1774:
1771:
1770:
1746:
1708:
1707:
1699:
1695:
1694:
1679:
1663:
1652:
1621:
1609:
1586:
1556:
1550:
1529:
1523:
1486:
1480:
1460:
1418:
1388:
1375:
1369:
1346:
1334:{\displaystyle \tau ^{2}={\text{id}}_{M}}
1325:
1320:
1310:
1304:
1292:{\displaystyle \tau ^{*}\omega =-\omega }
1271:
1265:
1233:
1201:
1181:
1155:
1132:
1100:
1068:
1039:
1019:
994:
939:
913:
912:
911:
896:
877:
866:
848:
840:
810:
809:
808:
793:
774:
763:
757:
737:
736:
735:
733:
699:
675:
645:
609:
577:
549:
529:
502:
477:
471:
438:
432:
409:
386:
381:
375:
337:
307:
294:
288:
261:
246:{\displaystyle \omega (X_{H},\cdot )=dH.}
216:
204:
181:
160:
154:
131:
111:
110:
109:
95:
59:
2223:Functional Analysis and Its Applications
640:if its graph intersects the diagonal of
1957:
1406:{\displaystyle H_{t}\in C^{\infty }(M)}
1176:be a compact Lagrangian submanifold of
325:{\displaystyle H_{t}\in C^{\infty }(M)}
86:be a closed (compact without boundary)
2206:"Periodic maps in symplectic topology"
1150:-dimensional symplectic manifold, let
119:{\displaystyle H:M\to {\mathbb {R} }}
7:
2042:
2040:
2018:
2016:
1926:Symplectomorphism#Arnold conjecture
1507:{\displaystyle \varphi _{t}:M\to M}
459:{\displaystyle \varphi _{t}:M\to M}
2115:
1834:, Yong-Geun Oh, Hiroshi Ohta, and
1611:
1389:
978:, named after Vladimir Arnold and
842:
308:
25:
2047:Arnold, Vladimir I., ed. (2005).
1014:in terms of the Betti numbers of
2335:Unsolved problems in mathematics
2057:, Heidelberg. pp. 284–288.
1574:{\displaystyle \varphi _{1}(L)}
959:{\displaystyle \varphi :M\to M}
629:{\displaystyle \varphi :M\to M}
2210:Funktsional. Anal. I Prilozhen
1895:
1883:
1857:
1845:
1802:
1766:
1760:
1748:
1712:
1685:
1642:
1633:
1627:
1614:
1568:
1562:
1498:
1438:
1426:
1400:
1394:
1244:
1212:
1114:
1102:
950:
918:
902:
815:
799:
745:{\displaystyle {\mathbb {F} }}
620:
591:
579:
450:
357:
345:
319:
313:
228:
209:
106:
73:
61:
1:
1581:intersects transversely with
2294:10.1007/978-3-0348-9217-9_23
1253:{\displaystyle \tau :M\to M}
1221:{\displaystyle \tau :M\to M}
486:{\displaystyle \varphi _{t}}
34:, named after mathematician
1901:{\displaystyle (M,\omega )}
1876:proved it in the case when
1863:{\displaystyle (M,\omega )}
1341:, whose fixed point set is
1120:{\displaystyle (M,\omega )}
1088:is Hamiltonian isotopic to
597:{\displaystyle (M,\omega )}
79:{\displaystyle (M,\omega )}
2351:
1169:{\displaystyle L\subset M}
976:Arnold–Givental conjecture
970:Arnold–Givental conjecture
495:Hamiltonian diffeomorphism
90:. For any smooth function
18:Arnold–Givental conjecture
2286:The Floer Memorial Volume
2204:Givental, A. B. (1989a),
2170:10.1155/S1073792804133941
659:{\displaystyle M\times M}
397:{\displaystyle X_{H_{t}}}
1516:Hamiltonian vector field
522:strong Arnold conjecture
148:Hamiltonian vector field
50:Strong Arnold conjecture
2190:, International Press,
1999:and the Conley index".
984:Lagrangian submanifolds
196:defined by the formula
139:{\displaystyle \omega }
27:Mathematical conjecture
2259:Oh, Yong-Geun (1992),
1993:
1941:Conley–Zehnder theorem
1902:
1864:
1809:
1719:
1668:
1595:
1575:
1539:
1508:
1469:
1451:be a smooth family of
1445:
1407:
1355:
1335:
1293:
1254:
1222:
1190:
1170:
1144:
1121:
1082:
1053:
1028:
1008:
960:
925:
885:
830:weak Arnold conjecture
822:
782:
746:
708:
684:
660:
630:
598:
568:Weak Arnold conjecture
558:
538:
511:
487:
460:
418:
398:
364:
326:
270:
247:
190:
170:
140:
126:, the symplectic form
120:
80:
2330:Hamiltonian mechanics
1994:
1903:
1865:
1810:
1720:
1648:
1596:
1576:
1540:
1538:{\displaystyle H_{t}}
1514:by flowing along the
1509:
1470:
1453:Hamiltonian functions
1446:
1444:{\displaystyle t\in }
1408:
1356:
1336:
1294:
1255:
1223:
1191:
1171:
1145:
1122:
1083:
1054:
1029:
1009:
961:
926:
862:
850:fixed points of
823:
759:
747:
709:
685:
661:
631:
599:
559:
539:
512:
488:
461:
419:
399:
365:
363:{\displaystyle t\in }
327:
271:
248:
191:
171:
169:{\displaystyle X_{H}}
141:
121:
81:
44:differential geometry
2288:, pp. 555–573,
1969:
1880:
1842:
1745:
1608:
1585:
1549:
1522:
1479:
1459:
1417:
1368:
1345:
1303:
1264:
1232:
1200:
1180:
1154:
1131:
1099:
1067:
1038:
1018:
993:
938:
839:
756:
732:
698:
674:
644:
608:
576:
548:
528:
501:
470:
431:
408:
374:
336:
287:
278:Hamiltonian function
260:
203:
180:
153:
130:
94:
58:
2325:Symplectic geometry
1936:Spectral invariants
88:symplectic manifold
40:symplectic geometry
2235:10.1007/BF01078943
2129:Fukaya et al. 2009
1989:
1898:
1860:
1805:
1715:
1591:
1571:
1535:
1504:
1465:
1441:
1403:
1351:
1331:
1289:
1250:
1218:
1186:
1166:
1143:{\displaystyle 2n}
1140:
1117:
1081:{\displaystyle L'}
1078:
1063:transversally and
1052:{\displaystyle L'}
1049:
1024:
1007:{\displaystyle L'}
1004:
980:Alexander Givental
956:
921:
818:
742:
704:
680:
656:
626:
594:
554:
534:
507:
483:
466:. Each individual
456:
414:
394:
360:
322:
266:
243:
186:
166:
136:
116:
76:
2303:978-3-0348-9948-2
2197:978-0-8218-5253-8
2153:(42): 2179–2269,
2090:Frauenfelder 2004
2072:978-3-540-20748-1
2050:Arnold's Problems
1594:{\displaystyle L}
1468:{\displaystyle M}
1354:{\displaystyle L}
1323:
1189:{\displaystyle M}
1027:{\displaystyle L}
851:
707:{\displaystyle M}
683:{\displaystyle M}
557:{\displaystyle M}
537:{\displaystyle M}
510:{\displaystyle M}
417:{\displaystyle M}
269:{\displaystyle H}
189:{\displaystyle M}
32:Arnold conjecture
16:(Redirected from
2342:
2306:
2279:
2253:
2217:
2200:
2181:
2172:
2162:
2132:
2125:
2119:
2112:
2106:
2099:
2093:
2086:
2077:
2076:
2044:
2035:
2034:
2032:
2020:
2011:
2010:
2008:
1998:
1996:
1995:
1990:
1988:
1987:
1982:
1976:
1962:
1907:
1905:
1904:
1899:
1874:Urs Frauenfelder
1869:
1867:
1866:
1861:
1814:
1812:
1811:
1806:
1801:
1800:
1795:
1783:
1782:
1777:
1724:
1722:
1721:
1716:
1711:
1703:
1698:
1684:
1683:
1667:
1662:
1626:
1625:
1600:
1598:
1597:
1592:
1580:
1578:
1577:
1572:
1561:
1560:
1544:
1542:
1541:
1536:
1534:
1533:
1513:
1511:
1510:
1505:
1491:
1490:
1474:
1472:
1471:
1466:
1450:
1448:
1447:
1442:
1412:
1410:
1409:
1404:
1393:
1392:
1380:
1379:
1360:
1358:
1357:
1352:
1340:
1338:
1337:
1332:
1330:
1329:
1324:
1321:
1315:
1314:
1298:
1296:
1295:
1290:
1276:
1275:
1259:
1257:
1256:
1251:
1227:
1225:
1224:
1219:
1195:
1193:
1192:
1187:
1175:
1173:
1172:
1167:
1149:
1147:
1146:
1141:
1126:
1124:
1123:
1118:
1091:
1087:
1085:
1084:
1079:
1077:
1062:
1058:
1056:
1055:
1050:
1048:
1033:
1031:
1030:
1025:
1013:
1011:
1010:
1005:
1003:
988:
965:
963:
962:
957:
930:
928:
927:
922:
917:
916:
901:
900:
884:
876:
852:
849:
827:
825:
824:
819:
814:
813:
798:
797:
781:
773:
751:
749:
748:
743:
741:
740:
719:Morse inequality
713:
711:
710:
705:
689:
687:
686:
681:
665:
663:
662:
657:
635:
633:
632:
627:
603:
601:
600:
595:
563:
561:
560:
555:
543:
541:
540:
535:
516:
514:
513:
508:
492:
490:
489:
484:
482:
481:
465:
463:
462:
457:
443:
442:
423:
421:
420:
415:
403:
401:
400:
395:
393:
392:
391:
390:
369:
367:
366:
361:
331:
329:
328:
323:
312:
311:
299:
298:
275:
273:
272:
267:
252:
250:
249:
244:
221:
220:
195:
193:
192:
187:
175:
173:
172:
167:
165:
164:
145:
143:
142:
137:
125:
123:
122:
117:
115:
114:
85:
83:
82:
77:
21:
2350:
2349:
2345:
2344:
2343:
2341:
2340:
2339:
2310:
2309:
2304:
2283:
2258:
2220:
2203:
2198:
2185:
2144:
2141:
2136:
2135:
2126:
2122:
2113:
2109:
2100:
2096:
2087:
2080:
2073:
2063:10.1007/b138219
2055:Springer Berlin
2046:
2045:
2038:
2022:
2021:
2014:
1977:
1967:
1966:
1964:
1963:
1959:
1954:
1949:
1922:
1878:
1877:
1840:
1839:
1787:
1769:
1743:
1742:
1732:
1675:
1617:
1606:
1605:
1583:
1582:
1552:
1547:
1546:
1525:
1520:
1519:
1482:
1477:
1476:
1457:
1456:
1415:
1414:
1384:
1371:
1366:
1365:
1343:
1342:
1319:
1306:
1301:
1300:
1267:
1262:
1261:
1230:
1229:
1198:
1197:
1178:
1177:
1152:
1151:
1129:
1128:
1097:
1096:
1089:
1070:
1065:
1064:
1060:
1041:
1036:
1035:
1016:
1015:
996:
991:
990:
986:
972:
936:
935:
892:
837:
836:
789:
754:
753:
730:
729:
717:In view of the
696:
695:
672:
671:
642:
641:
606:
605:
574:
573:
570:
546:
545:
526:
525:
499:
498:
473:
468:
467:
434:
429:
428:
426:diffeomorphisms
406:
405:
382:
377:
372:
371:
334:
333:
303:
290:
285:
284:
258:
257:
212:
201:
200:
178:
177:
156:
151:
150:
128:
127:
92:
91:
56:
55:
52:
36:Vladimir Arnold
28:
23:
22:
15:
12:
11:
5:
2348:
2346:
2338:
2337:
2332:
2327:
2322:
2312:
2311:
2308:
2307:
2302:
2281:
2271:(3): 309–314,
2256:
2255:
2254:
2229:(4): 287–300,
2201:
2196:
2183:
2140:
2137:
2134:
2133:
2120:
2107:
2103:Givental 1989b
2094:
2078:
2071:
2036:
2012:
1986:
1981:
1975:
1956:
1955:
1953:
1950:
1948:
1945:
1944:
1943:
1938:
1933:
1931:Floer homology
1928:
1921:
1918:
1917:
1916:
1897:
1894:
1891:
1888:
1885:
1871:
1870:semi-positive.
1859:
1856:
1853:
1850:
1847:
1838:proved it for
1829:
1826:
1823:Maslov indices
1816:
1804:
1799:
1794:
1791:
1786:
1781:
1776:
1773:
1768:
1765:
1762:
1759:
1756:
1753:
1750:
1741:proved it for
1731:
1728:
1727:
1726:
1714:
1710:
1706:
1702:
1697:
1693:
1690:
1687:
1682:
1678:
1674:
1671:
1666:
1661:
1658:
1655:
1651:
1647:
1644:
1641:
1638:
1635:
1632:
1629:
1624:
1620:
1616:
1613:
1590:
1570:
1567:
1564:
1559:
1555:
1532:
1528:
1518:associated to
1503:
1500:
1497:
1494:
1489:
1485:
1464:
1440:
1437:
1434:
1431:
1428:
1425:
1422:
1402:
1399:
1396:
1391:
1387:
1383:
1378:
1374:
1350:
1328:
1318:
1313:
1309:
1288:
1285:
1282:
1279:
1274:
1270:
1249:
1246:
1243:
1240:
1237:
1217:
1214:
1211:
1208:
1205:
1185:
1165:
1162:
1159:
1139:
1136:
1116:
1113:
1110:
1107:
1104:
1076:
1073:
1047:
1044:
1023:
1002:
999:
971:
968:
955:
952:
949:
946:
943:
932:
931:
920:
915:
910:
907:
904:
899:
895:
891:
888:
883:
880:
875:
872:
869:
865:
861:
858:
855:
847:
844:
817:
812:
807:
804:
801:
796:
792:
788:
785:
780:
777:
772:
769:
766:
762:
739:
703:
679:
668:Morse function
655:
652:
649:
625:
622:
619:
616:
613:
593:
590:
587:
584:
581:
569:
566:
553:
533:
506:
493:is a called a
480:
476:
455:
452:
449:
446:
441:
437:
413:
389:
385:
380:
359:
356:
353:
350:
347:
344:
341:
321:
318:
315:
310:
306:
302:
297:
293:
265:
254:
253:
242:
239:
236:
233:
230:
227:
224:
219:
215:
211:
208:
185:
163:
159:
135:
113:
108:
105:
102:
99:
75:
72:
69:
66:
63:
51:
48:
42:, a branch of
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2347:
2336:
2333:
2331:
2328:
2326:
2323:
2321:
2318:
2317:
2315:
2305:
2299:
2295:
2291:
2287:
2282:
2278:
2274:
2270:
2266:
2262:
2257:
2252:
2248:
2244:
2240:
2236:
2232:
2228:
2224:
2219:
2218:
2215:
2211:
2207:
2202:
2199:
2193:
2189:
2184:
2180:
2176:
2171:
2166:
2161:
2156:
2152:
2148:
2143:
2142:
2138:
2130:
2124:
2121:
2117:
2111:
2108:
2104:
2098:
2095:
2091:
2085:
2083:
2079:
2074:
2068:
2064:
2060:
2056:
2052:
2051:
2043:
2041:
2037:
2031:
2026:
2019:
2017:
2013:
2007:
2002:
1984:
1961:
1958:
1951:
1946:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1923:
1919:
1914:
1911:
1892:
1889:
1886:
1875:
1872:
1854:
1851:
1848:
1837:
1833:
1830:
1827:
1824:
1820:
1817:
1797:
1784:
1779:
1763:
1757:
1754:
1751:
1740:
1737:
1736:
1735:
1729:
1704:
1700:
1691:
1688:
1680:
1676:
1672:
1669:
1664:
1659:
1656:
1653:
1649:
1645:
1639:
1636:
1630:
1622:
1618:
1604:
1603:
1602:
1588:
1565:
1557:
1553:
1530:
1526:
1517:
1501:
1495:
1492:
1487:
1483:
1462:
1454:
1435:
1432:
1429:
1423:
1420:
1397:
1385:
1381:
1376:
1372:
1362:
1348:
1326:
1316:
1311:
1307:
1286:
1283:
1280:
1277:
1272:
1268:
1247:
1241:
1238:
1235:
1215:
1209:
1206:
1203:
1183:
1163:
1160:
1157:
1137:
1134:
1127:be a compact
1111:
1108:
1105:
1093:
1074:
1071:
1045:
1042:
1034:, given that
1021:
1000:
997:
985:
981:
977:
969:
967:
953:
947:
944:
941:
908:
905:
897:
893:
889:
886:
881:
878:
873:
870:
867:
863:
859:
853:
835:
834:
833:
831:
805:
802:
794:
790:
786:
783:
778:
775:
770:
767:
764:
760:
728:
724:
723:Betti numbers
720:
715:
701:
693:
690:, called the
677:
669:
653:
650:
647:
639:
638:nondegenerate
623:
617:
614:
611:
588:
585:
582:
567:
565:
551:
531:
523:
518:
504:
496:
478:
474:
453:
447:
444:
439:
435:
427:
411:
387:
383:
378:
354:
351:
348:
342:
339:
316:
304:
300:
295:
291:
281:
279:
263:
256:The function
240:
237:
234:
231:
225:
222:
217:
213:
206:
199:
198:
197:
183:
161:
157:
149:
133:
103:
100:
97:
89:
70:
67:
64:
49:
47:
45:
41:
37:
33:
19:
2285:
2268:
2264:
2226:
2222:
2213:
2209:
2187:
2160:math/0309373
2150:
2146:
2139:Bibliography
2123:
2110:
2097:
2049:
1960:
1913:Floer theory
1832:Kenji Fukaya
1819:Yong-Geun Oh
1733:
1363:
1094:
975:
973:
933:
829:
716:
692:Morse number
691:
637:
571:
521:
519:
494:
282:
276:is called a
255:
53:
31:
29:
2320:Conjectures
1059:intersects
2314:Categories
2251:0724.58031
2216:(4): 37–52
2030:1609.04776
2006:2202.00422
1947:References
1260:such that
1196:, and let
832:says that
636:is called
146:induces a
2243:123546007
1952:Citations
1893:ω
1855:ω
1836:Kaoru Ono
1673:
1650:∑
1646:≥
1637:∩
1619:φ
1612:#
1554:φ
1499:→
1484:φ
1424:∈
1390:∞
1382:∈
1308:τ
1287:ω
1284:−
1278:ω
1273:∗
1269:τ
1245:→
1236:τ
1213:→
1204:τ
1161:⊂
1112:ω
951:→
942:φ
890:
864:∑
860:≥
854:φ
843:#
787:
761:∑
752:, namely
651:×
621:→
612:φ
589:ω
475:φ
451:→
436:φ
343:∈
309:∞
301:∈
226:⋅
207:ω
134:ω
107:→
71:ω
1920:See also
1739:Givental
1075:′
1046:′
1001:′
2277:1179726
2179:2076142
2116:Oh 1995
1601:, then
725:over a
2300:
2275:
2249:
2241:
2194:
2177:
2069:
1910:gauged
1730:Status
828:. The
2239:S2CID
2155:arXiv
2025:arXiv
2001:arXiv
727:field
2298:ISBN
2192:ISBN
2151:2004
2067:ISBN
1364:Let
1299:and
1095:Let
989:and
974:The
934:for
572:Let
520:The
54:Let
30:The
2290:doi
2269:315
2247:Zbl
2231:doi
2165:doi
2059:doi
1670:dim
1455:on
887:dim
784:dim
694:of
670:on
497:of
404:on
176:on
2316::
2296:,
2273:MR
2267:,
2263:,
2245:,
2237:,
2227:23
2225:,
2214:23
2212:,
2208:,
2175:MR
2173:,
2163:,
2149:,
2081:^
2065:.
2053:.
2039:^
2015:^
1413:,
1361:.
1322:id
1092:.
714:.
564:.
517:.
332:,
280:.
46:.
2292::
2280:.
2233::
2182:.
2167::
2157::
2131:)
2127:(
2118:)
2114:(
2105:)
2101:(
2092:)
2088:(
2075:.
2061::
2033:.
2027::
2009:.
2003::
1985:n
1980:P
1974:C
1915:.
1896:)
1890:,
1887:M
1884:(
1858:)
1852:,
1849:M
1846:(
1825:.
1815:.
1803:)
1798:n
1793:P
1790:R
1785:,
1780:n
1775:P
1772:C
1767:(
1764:=
1761:)
1758:L
1755:,
1752:M
1749:(
1725:.
1713:)
1709:Z
1705:2
1701:/
1696:Z
1692:;
1689:L
1686:(
1681:i
1677:H
1665:n
1660:0
1657:=
1654:i
1643:)
1640:L
1634:)
1631:L
1628:(
1623:1
1615:(
1589:L
1569:)
1566:L
1563:(
1558:1
1531:t
1527:H
1502:M
1496:M
1493::
1488:t
1463:M
1439:]
1436:1
1433:,
1430:0
1427:[
1421:t
1401:)
1398:M
1395:(
1386:C
1377:t
1373:H
1349:L
1327:M
1317:=
1312:2
1281:=
1248:M
1242:M
1239::
1216:M
1210:M
1207::
1184:M
1164:M
1158:L
1138:n
1135:2
1115:)
1109:,
1106:M
1103:(
1090:L
1072:L
1061:L
1043:L
1022:L
998:L
987:L
954:M
948:M
945::
919:)
914:F
909:;
906:M
903:(
898:i
894:H
882:n
879:2
874:0
871:=
868:i
857:}
846:{
816:)
811:F
806:;
803:M
800:(
795:i
791:H
779:n
776:2
771:0
768:=
765:i
738:F
702:M
678:M
654:M
648:M
624:M
618:M
615::
592:)
586:,
583:M
580:(
552:M
532:M
505:M
479:t
454:M
448:M
445::
440:t
412:M
388:t
384:H
379:X
358:]
355:1
352:,
349:0
346:[
340:t
320:)
317:M
314:(
305:C
296:t
292:H
264:H
241:.
238:H
235:d
232:=
229:)
223:,
218:H
214:X
210:(
184:M
162:H
158:X
112:R
104:M
101::
98:H
74:)
68:,
65:M
62:(
20:)
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