Math 6441

Algebraic Topology

Fall 2012
-
----------------------------------------M.C. Escher
News: Welcome to Math 6441!

Class Meetings

 Tuesday and Thursday, 1:35-2:55 pm, Skiles 254.

Book

Office Hours

 In Skiles 244, Tuesday and Thursday after class and by appointment.
Jamie Conway, Monday 1-2, Skiles 165
Robert Krone, Wednesday 4-5, Skiles 147

Problem Session

 In Skiles 005, Wednesday 4-5.

Homework

 There will be weekly homework assignments. Students should work in groups of (approximately) five people. Each student should write up (approximately) one fifth of the problems for the group. Each paper should be labeled clearly with the author at the top and the other group members underneath.

Graders

Grading

 Grades will be tabulated according to the following scheme:

Homework 50%, Midterm 20%, Final 30%.

Weekly Schedule

 Note: The class notes below are in large part abridged portions of our textbook, by Allen Hatcher. I take no credit for originality.

Week Dates Topics Text Sections Homework Lectures Notes
1 Aug 21/23 Cell complexes Chapter 0 p. 18 # 1,2,3,9,10,14,16,17,18,20 Week 1
2 Aug 28/30 Fundamental group Section 1.1 p. 38 # 6,7,8,9,10,12,16,17,18,20 Week 2
3 Sep 4/6 Van Kampen's theorem Section 1.2 p. 52 # 1,3,7,8,9,11,14,16,17,22 Week 3
4 Sep 11/13 Covering spaces Section 1.3 - Week 4
5 Sep 18/20 Classifying spaces Section 1.3 p. 79 # 4, 5, 9, 10, 11, 12, 13, 14, 18, 19 Week 5
6 Sep 25/27 Homology Section 2.1 - Substitute teacher
7 Oct 2/4 Homology Section 2.1 p. 131 # 3,4,6,7,8 Week 7 Exam
8 Oct 9/11 Homology Section 2.1 p. 131 # 2,9,11, 12, 13 Week 8
9 Oct 18 Relative homology Section 2.1 p. 131 # 15, 16, 17, 18, 20 Fall break
10 Oct 23/25 Excision / Mayer-Vietoris Section 2.1 p. 131 # 19,22,23,28,29 Weeks 9-10
11 Oct 30/Nov 1 Applications Section 2.2 p. 176 # 2,8,10
p. 184 # 2,5 		Week 11
12 Nov 6/8 Cohomology Section 3.1 p. 204 # 5,6,8,9,13 Week 12
13 Nov 13/15 Products Section 3.2 - Weeks 13 and 14
14 Nov 20 Products Section 3.2 p. 228 # 1,3,4,5,7,10,11,14,15,18 Thanksgiving
15 Nov 27/29 Poincaré duality Section 3.3 p. 258 # 7,10,11,24,25,26 Week 15
16 Dec 4/6 Poincaré duality Section 3.3 - Course notes Exam

Resources

---Algebraic Topology, Allen Hatcher

---Lecture Notes in Algebraic Topology, James F. Davis and Paul Kirk

---Algebraic Topology Class Notes, Denis Sjerve (notes by Benjamin Young)

---Algebraic Topology I, Tim Perutz

---algebraic topology, Michael Hopkins (notes by Eva Belmont and Akhil Mathew)

---Algebraic Topology, Len Evans and Rob Thompson

---Spectral Sequences in Algebraic Topology, Allen Hatcher

---Homology: An idea whose time has come, Barry A. Cipra

---Assembling geometric data using statistics for topology, Peter Bubenik

---Barcodes: The Persistent Topology of Data, Robert Ghrist

---Persistent Homology - a Survey, Herbert Edelsbrunner and John Harer

---Computing Persistent Homology, Afra Zomorodian and Gunnar Carlsson

---A History of Duality in Algebraic Topology, James Becker and Daniel Gottlieb

---Duality in Mathematics and Physics, Sir Michael Atiyah

---T-Square

---Georgia Tech Honor Code