## MA 651: Topology II

Kate Ponto
Spring 2021

Syllabus

### Announcements

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.

Office hours: Monday 1-2, Thursday 2:30-3:30, and Friday 11-12

### Homework

(Pages from Lee)
2/3 7-1, 7-2a, 7-3, 7-2b, 7-6 183-191, 192-195, 197-199, 200-203
2/10 7-4, 7-10, 7-5, 7-9 204-208, 217-220, 221-224
2/17 (For these problems you can assume the fundamental group is non trivial) 8-1, 8-6, 8-4, 8-7, 8-8 224-227, 227-229, 277-280, 281-286
2/24 8-11, 11-3, 11-4, 11-7 (Some reminders for torus and klein bottle.) 11-2 287-289, 290-291, 292-294
3/3 11-12, 11-13, 11-14, 11-15 295-297, 298-301
3/10 11-18, 11-19, 11-20, 11-9 (remember to show evenly covered!) 302, 307-308, 309-311
3/17 11-10, 11-11, 11-21 (you can use cor 10.17 without proof for now.) 311-314, 315-317
3/24 12-2, 12-3, 12-4, 12-8, 12-12 318-322, 233-235, 236-239
3/31 9-1, 9-2, 9-4a 240-244, 251-253, 253-264
4/7 10-1, 10-2, 10-5, 10-6, 10-9 268-273, 265-267
4/14 6-1, 6-3, 6-6, 10-11, 10-13 159-172, 264-268, 173-180
4/21 10-3, 9-8 (rank and basis are defined on p. 245), 13-1, 13-2 (You can assume that the ith homology of the n sphere is isomorphic to the integers if i is 0 or n and zero otherwise) 339-343, 344-347, 348-352
4/28 13-6, 13-7 (You can assume that the nth homology of the n sphere is isomorphic to the integers), 13-5 353-356, 356-360, 361-364
5/5 Homology of spaces