Combinatorial Methods in Algebraic Topology

SPWM Mini-Course, June 29-July 10, 2009


Current set of notes

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

Presentation schedule   


Last updated: 9 July 2009