MA 651: Topology II

Kate Ponto
Spring 2019

Syllabus

Announcements



Office hours will be M 11-12, T 3:30-4:30 and F 1:30-2:30.

The primary textbook for this class will be Introduction to Topological Manifolds by Lee. (It is available through SpringerLink - check the library website!)

Algebraic Topology by Hatcher and Topology by Munkres can also be useful references.

Homework



Due Assignment Reading
(Pages from Lee)
1/16 7-1, 7-10, 7-2 183 - 195, 197 - 199
1/23 7-3, 7-6, 7-4, 7-5, 7-9 199 - 208, 217 - 221
1/30 7-11, 8-1 (you can use the fact that the circle is not simply connected), 8-4, 8-6 221 - 226, 227 - 229
2/6 8-7, 8-8, 8-11 277 - 283
2/13 11-1, 11-4, 11-7, 11-10, 11-13 283 - 291
2/20 11-12, 11-14, 11-15, 11-20 (A universal cover is a simply connected covering space) 292 - 302
2/27 11-17, 11-18, 11-19, 11-21 (you can use 10.17 without proof right now) 307 - 318
3/6 12-1, 12-2, 12-4, 12-12, 12-13 (You can use the computation of the fundamental group of a wedege of circles without proof right now.) 233 - 241
3/20 9-1, 9-2, 9-4a, 10-1, 10-2, 10-6 251 - 257, 261 - 264, 268 - 273
3/27 10-5, 10-7, 10-11 257 - 261, 264 - 268, 339 - 347
4/3 10-3, 10-10, 10-13, 10-20 347 - 351
4/10 13-2, 13-3, 13-4 (you can use that the homology of a n dimensional sphere is a Z in dimension n and 0 and trivial in other degrees), 13-11, exercise (not problem!) 13.10 351 - 359
4/17 13-6, 13-7, 13-8 359 - 366
4/24 Homological Algebra Problems