## MA 651: Topology II

Kate Ponto
Spring 2017

Syllabus

### Announcements

It looks like subgroups of free groups are free might not be in Lee's book. Alternative references are:
Hatcher section 1.A
Munkres chapter 14

Office hours will be MTF 1-2 MF 1-2:30.

The primary textbook for this class will be Introduction to Topological Manifolds by Lee. (It is available through SpringerLink.)

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

### Homework

Due Assignment Reading
(Pages from Lee)
4/26 6-1, 6-2, 6-3, 6-6 178 - 179, 355 - 364
4/19 13-6, 13-7 351 - 355, 159 - 178
4/12 13-1, 13-2 (You can assume the n dim sphere has non trivial homology in dimension n) 344 - 350
4/5 10-11, 10-15, 10-9, 10-20, 9-9 257 - 261, 244 - 248, 339 - 344
3/29 10-1, 10-21, 10-2, 10-6, 10-5 268 - 273, 127 - 142
3/22 12-9, 12-17, 12-21, 9-1, 9-2, 9-4a 241 - 244, 251 - 257, 261 - 264
3/8 11-20, 12-1, 12-2, 12-7, 12-12 311 - 322, 233 - 241
3/1 11-17, 11-18 307 - 311
2/22 11-12, 11-14, 12-3, 12-4(a) 294 - 302
2/15 11-2, 11-3, 11-4, 11-10 284 - 293
2/8 8-1, 8-2 (You may assume the circle is not simply connected.) 8-11 (a-c), 8-6 225 - 229, 277 - 283
2/1 7-2, 7-6, 7-4, 7-9, 7-11, 7-12 200 - 208, 217 - 224
1/26 ex. 7.6, ex. 7.14(a), 7-3, 7-5 (You can use the square lemma!) 191 - 199
1/18 3-8, 3-10, 7-1, 7-10 (A space is contractible if the identity map is homotopic to the constant map at a point.) Chapter 3, 183 - 190