Math 6520 Algebraic Topology

Instructor: Mladen Bestvina

Office: JWB 210

Web page: http://www.math.utah.edu/~bestvina/6520

Office Hours: by appointment

Textbook: Algebraic Topology, by Allen Hatcher, Cambridge University Press. You can download a copy from Hatcher's web page

Time: MWF 10:45-11:35

Room: JWB 333

The grades will be based on homework, class presentations and the final exam.

You can contact me by email.

Homework 1, due Jan 26: #1,15,23 from Ch 0

Homework 2, due Feb 9: sec 1.1: #6, 16 a,b,f (and c for “extra credit”), sec 1.2: #3,7,8

I also recommend picking one or two of 9,10,11,12,13,14,16,21,22 from 1.2 and thinking about them. #22 is particularly useful.

Homework 3, due Feb 25: sec 1.3: #14,20,21. Hint on #20: Understand the universal cover and its covering group. Find non-normal subgroup of finite index that are [not] abelian.

If you have an interest in pursuing topology, you should read sections 1.A and 1.B and work on corresponding exercises. Particularly important are concepts of the Cayley graph (or a complex) and applications of covering spaces in the algebra of free groups.

Homework 4, due March 11 (this time it is not a mistake -- no class on March 6 and March 9): Section 2.1: #4,6,8,19,20. Hint for #19,20: Use the long exact sequence of a pair (X,A) for a conveniently chosen A, and excision.

Homework 5, due March 30: Section 2.2: #1,2,13,19,23.

Homework 6, due April 15: Section 2.2: #25,43, Section 2.3: #4 (read about split exact sequences), Section 2.B: #2,8.

Take home final, due May 8.