__Combinatorial Methods in Algebraic Topology__

SPWM Mini-Course, June 29-

__Monday, June 29:__ Simplices and simplicial complexes

Homework: Exercises 1.2 and 1.4 in the notes
(you may turn in any of the others you want me to look at)

For tomorrow: Look over the following book chapter to see some
of the main ideas of topology:

Topology Now!
(Chapter 1 on the idea of topology)

If you are thinking about a project topic related to today’s
material, you might look at:

Notes on
polyhedral and 3-dimensional geometry

__Tuesday, June 30:__ Topological spaces and their relationship with simplicial
complexes

Homework: Exercise 2.6 in the notes; 2.9 is
recommended, and you might also look at 2.7 (after reading the paragraph before
it). Again, you may turn in any others
you would like me to look at, especially the two from the end of class.

For Thursday: Look over the handout on another
perspective on topology, topological equivalence, and invariants.

There are lots of possibilities for project
topics here, and I have books you can look though if you are interested.

__Thursday, July 2:__ Homeomorphism, invariants, and homotopy

Homework: Exercises 2.7, 3.4, 3.5, and 4.3.

For tomorrow: Look at the first couple sections of Chapter 3:

Topology: A
Geometric Approach

Section
3.1 is especially useful for those needing a review of groups.

Again, there are lots of project ideas here: for
example, other invariants, or classification of various kinds of spaces.

__Friday, July 3:__ Fundamental groups

Homework: Exercises 4.4 and 4.5

For Monday: Read the handout on fundamental
groups.

__Monday, July 6:__ Homotopy equivalence and more on
fundamental groups

Homework: Be sure you have your project groups
and topics by tomorrow.

For tomorrow: Look at the following paper on
simplicial sets.

__Tuesday, July 7:__ From simplicial complexes to simplicial sets

Homework: Work on presentations.

For Thursday: Look at the first three sections
of the following paper. (This was written by a
student in an REU last summer!)

__Thursday, July 9:__ Categories and functors

Homework: Finish presentations.

Friday, July 10: Presentation day

Last
updated: 9 July 2009