## Algebraic Topology, Spring 2019

#### Day/Time: MWF 12:20pm – 1:10pm

Location: Phillips 301

Syllabus: click here

### Homework:

Assignment 1 (due 1/23): Chapter 0, Problems 1, 2, 3, 5, 6, 12

Assignment 2 (due 1/30): Chapter 0, Problems 10, 11, 14, 16, 18, 24

Assignment 3 (due 2/8): Section 1.2, Problems 4, 6, 9; Section 1.3, Problems 4, 6, 7, 9, 16, 27

Assignment 4 (due 2/15): Section 2.1, Problems 1, 2, 3, 5, 8

Assignment 5 (due 2/25): Section 2.1, Problems 12, 14, 15, 16, 18

Assignment 6 (complete before the end of break): Read Section 2.A in Hatcher (and for those who missed lecture on 3/8, also read pages 137-141)

Assignment 7 (due 3/29): Section 2.2, Problems 1, 2, 22, 23, 29, and compute the homology of the space obtain by removing a knot K from the 3-sphere (a knot is a smoothly embedded copy of the 1-sphere; important for this problem is that K is homeomorphic to the 1-sphere, and has a deformation retract neighborhood that is homeomorphic to the interior of the solid torus)

Assignment 8 (due 4/17): Section 3.1, Problems 3, 5; Section 3.2, Problems 1, 2, 7 (read the proof of, and then use, Theorem 3.19 from the online version of the book), 10