Topics in Algebraic Topology

Department: 
Math
Course Number: 
8803-BEA
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Not regularly scheduled

Special topics course on Algebraic Topology, offered in Fall 2020 by Jonathan Beardsley.

Prerequisites: 

MATH 6441

Course Text: 

-Davis and Kirk "Lecture Notes in Algebraic Topology" (freely available on author's website: https://jfdmath.sitehost.iu.edu/teaching/m623/book.pdf)

-Hatcher "Algebraic Topology" (freely available on author's website: https://pi.math.cornell.edu/~hatcher/AT/ATpage.html) 

-May "A Concise Course in Algebraic Topology" (freely available on author's website: https://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf)

-Hatcher "Spectral Sequences" (freely available on author's website: https://pi.math.cornell.edu/~hatcher/AT/SSpage.html) 

Topic Outline: 

CW complexes and CW approximation

Higher homotopy groups

Fibrations and fiber sequences

Classifying spaces, the bar construction and group cohomology

Homology and cohomology theories (K-theory, bordism)

Spectral Sequences

Loop spaces and the A-infinity operad