Columbia University G4308
Algebraic topology II
Basic information
| Call number: | 71246
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| Room/Time: | MW 2:40pm-3:55pm, 507 Math |
| Discussions: | Wednesdays 6-7:30pm in 528 Math |
| Instructor: | Mikhail Khovanov |
| Office: | 620 Math |
| Office Hours: | Walk-in |
| E-mail: | 
|
| Webpage: | www.math.columbia.edu/~khovanov/gradalgtopII | |
| |
Syllabus
Cohomological operations
Spectral sequences
K-theory
Homework
Homework 1, due
Wednesday, February 5.
Homework 2, due
Wednesday, February 26.
Homework 3, due
Monday, March 24.
Homework 4, due
Wednesday, April 23.
Homework 5, due
Wednesday, May 7.
Resources
Homotopic topology by A.Fomenko, D.Fuchs, and V.Gutenmacher.
Chapters 1 and 2: Homotopy and Homology,
Chapter 3: Spectral sequences,
Chapter 4: Cohomology operations,
Chapter 5: The Adams spectral sequence,
Index.
Algebraic
Topology, by Alan Hatcher. For Steenrod squares see Section 4.L.
Spectral
Sequences in Algebraic
Topology, by Alan Hatcher.
Vector
Bundles and K-Theory, by Alan Hatcher.
Double page
format.
Additional resources
Michael Hopkins Notes on Steenrod operations
Chapter 2
of "Cohomology operations in homotopy theory" by Mosher and Tangora.
Boris Botvinnik
Lecture Notes on
Algebraic Topology.
James F. Davis and Paul Kirk
Lecture Notes in Algebraic Topology.
Peter May
Concise Course in Algebraic Topology.
Algebraic Topology II by Mark Behrens.