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: MF 3:15-4:45

Room: LCB 323

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

You can contact me by email.

Homework 1, due Jan 27: p.18: #1,2,9,15,18 (look up the definition of the join; you are allowed to use "associativity", i.e. that (A*B)*C and A*(B*C) are naturally homeomorphic).

Homework 2, due Feb 10: p.38: #6,7,16; p.52: #2,9,11. In addition, for extra credit, find a presentation of the fundamental group of the complement of the figure 8 knot, pictured here and prove that this knot is different from the trefoil. Hint: Show that the trefoil group has a homomorphism onto the symmetric group S₃, while the figure 8 group does not.

Homework 3, due Feb 24: p.80: #11,12,14,18,21 and 13 (extra credit). Hint on #12: The group with the suggested presentation is the symmetry group of the square. Also p.131:#6,8.

Homework 4, due Mar 23: p.155: #2,3,7,9b,9c,28,30d,36; p.176: #1.

Take home final, due May 10.