Math 6441Algebraic TopologySpring 2019- |
----------------------------------------M.C. Escher |
Week | Dates | Topics | Text Sections | Homework | Lectures | Notes | ||
1 | Jan 7 | Intro / Spaces | Chapter 0 | p. 18 #1,2,3 | 16,20 | |||
2 | Jan 14 | Fundamental group | Section 1.1 | p. 18 #23 | p. 38 #6 | #7,8,9 | ||
3 | Jan 21 | Van Kampen's theorem | Section 1.2 | p. 38 #16 | p. 38 #19 | MLK day | ||
4 | Jan 28 | Covering spaces | Section 1.3 | p. 52 #1,3,4 | #8,9,11 | p. 79 #1,4,10 | ||
5 | Feb 4 | Classifying spaces | Section 1.3 | p. 79 #9 | #12,14 | 18,19 | ||
6 | Feb 11 | Homology | Section 2.1 | p. 96 #1,2 | p.131 #4,5 | #7,8,9 | ||
7 | Feb 18 | Relative homology | Section 2.1 | p. 131 # 11,12,13 | #17,21 | #22 | ||
8 | Feb 25 | Excision / Mayer-Vietoris | Section 2.1 | p. 131 # 28 | # 29 | p. 176 #2,6 | ||
9 | Mar 4 | Applications | Section 2.1 | p. 176 #8 | p. 184 #5 | p. 155 #8,22,23,24 | ||
10 | Mar 11 | Cohomology | Section 2.1 | - | p. 204 # 5,6 | #10 | ||
Spring Break | ||||||||
11 | Mar 25 | Cup product | Section 2.2 | - | p. 204 #8,9 | p. 228 #1,3,7 | ||
12 | Apr 1 | Poincaré duality | Section 3.1 | - | p. 228 #10,11,12 | p. 257 #6,24,25 | Cup & Cap | |
13 | Apr 8 | Spectral sequences | Section 3.2 | p. 257 #10,11,26 | below | Spectral Sequences | ||
14 | Apr 15 | Spectral sequences | Section 3.2 | below | below | |||
15 | Apr 22 | Spectral sequences | Section 3.3 |
---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
---Introduction to Spectral Sequences, Michael Hutchings
---Lyndon-Hochschild-Serre Spectral Sequence - Application, Benjamin Ruppik
---The topology of fiber bundles, Ralph L. Cohen
---Spectral sequences via examples, Antonio Díaz Ramos
---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
---Visualizing Poincare Duality, Lucien Clavier
---On proof and progress in mathematics, William Thurston