246:
50:
in a series of four long papers. Much of the analytical complexity connected to this invariant comes from properly counting multiply covered pseudoholomorphic curves so that the result is invariant of the choice of almost complex structure. The crux is a topologically defined index for
144:. The ECH index is a version of Taubes's index for the cylindrical case, and again, the curves are pseudoholomorphic with respect to a suitable almost complex structure. The result is a topological invariant of
142:
91:
287:
280:
116:, and whose differential counts certain embedded pseudoholomorphic curves and multiply covered pseudoholomorphic cylinders with "ECH index" 1 in
316:
273:
178:
62:
47:
306:
40:
105:
29:
201:
119:
68:
253:
46:
Taubes proved the information contained in this invariant is equivalent to invariants derived from the
311:
108:-like invariant; namely, it is the homology of a chain complex generated by certain combinations of
33:
210:
109:
174:
173:. First International Press Lecture Series. Vol. 2. Somerville, MA: International Press.
257:
220:
98:
232:
188:
228:
196:
184:
166:
25:
149:
58:
52:
300:
17:
101:
36:
224:
199:(2010). "Embedded contact homology and Seiberg-Witten Floer cohomology I.".
39:, where the curves are holomorphic with respect to an auxiliary compatible
43:. (Multiple covers of 2-tori with self-intersection 0 are also counted.)
245:
51:
pseudoholomorphic curves which controls embeddedness and bounds the
215:
171:
Seiberg Witten and Gromov invariants for symplectic 4-manifolds
261:
65:
of this work to noncompact four-manifolds of the form
122:
71:
136:
85:
148:, which Taubes proved is isomorphic to monopole
281:
8:
152:, a version of Seiberg–Witten homology for
288:
274:
214:
130:
129:
121:
79:
78:
70:
28:counts embedded (possibly disconnected)
7:
242:
240:
137:{\displaystyle Y\times \mathbb {R} }
86:{\displaystyle Y\times \mathbb {R} }
260:. You can help Knowledge (XXG) by
169:(2000). Wentworth, Richard (ed.).
14:
244:
1:
317:Differential geometry stubs
333:
239:
59:Embedded contact homology
48:Seiberg–Witten equations
41:almost complex structure
30:pseudoholomorphic curves
225:10.2140/gt.2010.14.2497
202:Geometry & Topology
106:symplectic field theory
61:is an extension due to
256:-related article is a
138:
87:
254:differential geometry
139:
112:of a contact form on
88:
120:
69:
307:Symplectic topology
134:
83:
269:
268:
63:Michael Hutchings
324:
290:
283:
276:
248:
241:
236:
218:
209:(5): 2497–2581.
197:Taubes, Clifford
192:
167:Taubes, Clifford
143:
141:
140:
135:
133:
92:
90:
89:
84:
82:
22:Gromov invariant
332:
331:
327:
326:
325:
323:
322:
321:
297:
296:
295:
294:
195:
181:
165:
162:
118:
117:
67:
66:
26:Clifford Taubes
12:
11:
5:
330:
328:
320:
319:
314:
309:
299:
298:
293:
292:
285:
278:
270:
267:
266:
249:
238:
237:
193:
179:
161:
158:
150:Floer homology
132:
128:
125:
81:
77:
74:
53:Fredholm index
13:
10:
9:
6:
4:
3:
2:
329:
318:
315:
313:
310:
308:
305:
304:
302:
291:
286:
284:
279:
277:
272:
271:
265:
263:
259:
255:
250:
247:
243:
234:
230:
226:
222:
217:
212:
208:
204:
203:
198:
194:
190:
186:
182:
180:1-57146-061-6
176:
172:
168:
164:
163:
159:
157:
155:
151:
147:
126:
123:
115:
111:
107:
103:
100:
97:is a compact
96:
75:
72:
64:
60:
56:
54:
49:
44:
42:
38:
35:
31:
27:
23:
19:
262:expanding it
251:
206:
200:
170:
153:
145:
113:
104:. ECH is a
94:
57:
45:
21:
15:
312:4-manifolds
110:Reeb orbits
18:mathematics
301:Categories
160:References
102:3-manifold
37:4-manifold
34:symplectic
216:0811.3985
127:×
76:×
93:, where
233:2746723
189:1798809
99:contact
231:
187:
177:
20:, the
252:This
211:arXiv
32:in a
258:stub
175:ISBN
221:doi
24:of
16:In
303::
229:MR
227:.
219:.
207:14
205:.
185:MR
183:.
156:.
55:.
289:e
282:t
275:v
264:.
235:.
223::
213::
191:.
154:Y
146:Y
131:R
124:Y
114:Y
95:Y
80:R
73:Y
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.