Math 6441Algebraic TopologyFall 2012 
M.C. Escher 


Homework 50%, Midterm 20%, Final 30%.
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 / MayerVietoris  Section 2.1  p. 131 # 19,22,23,28,29  Weeks 910  
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 
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
TSquare