27:
218:
Chapter 5 is titled "plats and links". It moves from 2-dimensional topology to 3-dimensional topology, and is more speculative, concerning connections between braid groups, 3-manifolds, and the classification of links. It includes also an analog of
Alexander's theorem for plats, where the number of
360:
Knots, Braids, and
Mapping Class Groups — Papers Dedicated to Joan S. Birman: Proceedings of a Conference on Low Dimensional Topology in Honor of Joan S. Birman's 70th Birthday, March 14-15, 1998, Columbia University, New York, New
242:
Reviewer Lee
Neuwirth calls the book "most readable", "a nice mix of known results on the subject and new material". Whitten describes it as "thorough, skillfully written" and "a pleasure to read".
223:
of a given link. The appendix provides a list of 34 open problems. By the time Wilbur
Whitten wrote his review, in June 1975, a handful of these had already been solved.
148:
for braids, the question of determining whether two different-looking braid presentations really describe the same group element. It also describes the braid groups as
287:
246:
finds it "remarkable" that while covering the subject with full mathematical rigor, Birman has preserved the intuitive appeal of some of its earliest works.
125:, this was the first book devoted to them. It has been described as a "seminal work", one that "laid the foundations for several new subfields in topology".
175:, important in this area because conjugate braids close off to form the same link, and on the "algebraic link problem" (not to be confused with
77:
179:) in which one must determine whether two links can be related to each other by finitely many moves of a certain type, equivalent to the
159:
The next three chapters present connections of braid groups to three different areas of mathematics. Chapter 2 concerns applications to
472:
369:
137:
462:
212:
457:
111:
55:
231:
This is a book for advanced mathematics students and professionals, who are expected to already be familiar with
99:
26:
236:
145:
167:
that every knot or link can be formed by closing off a braid, and provides the first complete proof of the
164:
467:
188:
136:
is organized into five chapters and an appendix. The first introductory chapter defines braid groups,
200:
204:
232:
149:
365:
350:
172:
114:
and
University of Tokyo Press, as volume 82 of the book series Annals of Mathematics Studies.
72:
434:
358:
296:
199:'s free differential calculus, the Magnus representation of free groups and the Gassner and
337:
438:
385:
354:
333:
184:
140:, and the use of configuration spaces to define braid groups on arbitrary two-dimensional
107:
278:
243:
192:
176:
168:
451:
364:, AMS/IP studies in advanced mathematics, American Mathematical Society, p. ix,
220:
180:
118:
301:
239:. Although it is not a textbook, it could possibly be used for graduate seminars.
160:
103:
95:
37:
215:, and plats, braids closed off in a different way than in Alexander's theorem.
328:
208:
153:
122:
171:
on equivalence of links formed in this way. It also includes material on the
196:
91:
141:
429:
219:
strands of the resulting plat turns out to be determined by the
117:
Although braid groups had been introduced in 1891 by
71:
61:
51:
43:
33:
237:presentations of groups by generators and relators
288:Bulletin of the American Mathematical Society
8:
19:
418:
416:
414:
412:
410:
408:
406:
384:Serenevy, Amanda Katharine (August 2006),
25:
18:
317:
315:
313:
311:
300:
273:
271:
269:
267:
265:
263:
261:
259:
203:of braid groups. Chapter 4 concerns the
47:Braid groups in low-dimensional topology
20:Braids, Links, and Mapping Class Groups
425:Braids, Links, and Mapping Class Groups
324:Braids, Links, and Mapping Class Groups
283:Braids, Links, and Mapping Class Groups
255:
134:Braids, Links, and Mapping Class Groups
87:Braids, Links, and Mapping Class Groups
16:Mathematical monograph on braid groups
393:, Mathematical Association of America
7:
14:
156:and of multiply-punctured disks.
144:. It provides a solution to the
357:; Lin, Xiao-Song, eds. (2001),
302:10.1090/s0002-9904-1976-13937-7
110:, and published in 1974 by the
1:
423:Neuwirth, L. P., "Review of
322:Whitten, Wilbur, "Review of
106:, based on lecture notes by
281:(January 1976), "Review of
489:
121:and formalized in 1925 by
112:Princeton University Press
98:and their applications in
56:Princeton University Press
24:
473:Low-dimensional topology
387:Joan Birman and Topology
100:low-dimensional topology
213:Lickorish twist theorem
463:1975 non-fiction books
227:Audience and reception
201:Burau representations
189:representation theory
187:. Chapter 3 concerns
205:mapping class groups
138:configuration spaces
102:. It was written by
355:Menasco, William W.
165:Alexander's theorem
150:automorphism groups
21:
233:algebraic topology
90:is a mathematical
458:Mathematics books
173:conjugacy problem
83:
82:
78:978-0-691-08149-6
480:
442:
441:
420:
401:
400:
399:
398:
392:
381:
375:
374:
347:
341:
340:
319:
306:
305:
304:
275:
207:of 2-manifolds,
185:link complements
63:Publication date
29:
22:
488:
487:
483:
482:
481:
479:
478:
477:
448:
447:
446:
445:
422:
421:
404:
396:
394:
390:
383:
382:
378:
372:
349:
348:
344:
321:
320:
309:
277:
276:
257:
252:
229:
193:Fox derivatives
191:, and includes
177:algebraic links
131:
108:James W. Cannon
64:
17:
12:
11:
5:
486:
484:
476:
475:
470:
465:
460:
450:
449:
444:
443:
402:
376:
370:
342:
307:
254:
253:
251:
248:
244:Wilhelm Magnus
228:
225:
169:Markov theorem
130:
127:
81:
80:
75:
69:
68:
65:
62:
59:
58:
53:
49:
48:
45:
41:
40:
35:
31:
30:
15:
13:
10:
9:
6:
4:
3:
2:
485:
474:
471:
469:
466:
464:
461:
459:
456:
455:
453:
440:
436:
432:
431:
426:
419:
417:
415:
413:
411:
409:
407:
403:
389:
388:
380:
377:
373:
371:9780821829660
367:
363:
362:
356:
352:
346:
343:
339:
335:
331:
330:
325:
318:
316:
314:
312:
308:
303:
298:
294:
290:
289:
284:
280:
274:
272:
270:
268:
266:
264:
262:
260:
256:
249:
247:
245:
240:
238:
234:
226:
224:
222:
221:bridge number
216:
214:
210:
206:
202:
198:
194:
190:
186:
182:
181:homeomorphism
178:
174:
170:
166:
162:
157:
155:
151:
147:
143:
139:
135:
128:
126:
124:
120:
119:Adolf Hurwitz
115:
113:
109:
105:
101:
97:
93:
89:
88:
79:
76:
74:
70:
66:
60:
57:
54:
50:
46:
42:
39:
36:
32:
28:
23:
468:Braid groups
428:
424:
395:, retrieved
386:
379:
359:
351:Gilman, Jane
345:
327:
323:
295:(1): 42–46,
292:
286:
282:
241:
230:
217:
158:
146:word problem
133:
132:
116:
96:braid groups
86:
85:
84:
209:Dehn twists
161:knot theory
154:free groups
104:Joan Birman
38:Joan Birman
452:Categories
439:0305.57013
397:2021-01-02
329:MathSciNet
279:Magnus, W.
250:References
123:Emil Artin
142:manifolds
92:monograph
52:Publisher
211:and the
338:0375281
44:Subject
437:
430:zbMATH
368:
336:
163:, via
129:Topics
34:Author
391:(PDF)
366:ISBN
361:York
235:and
195:and
73:ISBN
67:1974
435:Zbl
427:",
326:",
297:doi
285:",
197:Fox
183:of
152:of
94:on
454::
433:,
405:^
353:;
334:MR
332:,
310:^
293:82
291:,
258:^
299::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
