Algebraic Structures 509A: Homological algebra; Spring 2017

Instructor: Julia Pevtsova

Place: Padelford Hall, 401

Time: 9:30-10:20, MWF

Office Hours: by appointment (that is, I am happy to talk between classes, just need an advance notice)

Course Description.  An introductory course on homological algebra. 

Topics:

·         Chain complexes, homotopies, homology and long exact sequence in homology

·         Resolutions, derived functors, Ext and Tor. Koszul complexes

·         Group (co)homology

·         Triangulated and derived categories

·         Spectral sequences or open topic depending on the class interests

 

Grading system. Based on homework and class presentations.

 

Textbook.  C. Weibel,  An introduction to homological algebra

Other references.

General/comprehensive homological algebra texts:

1.      J. Rotman, An introduction to homological algebra, electronic version (UW restricted)

2.      H. Cartan, S Eilenberg, Homological algebra (even though outdated, this is  a classic where the foundations of the subject were laid out)

3.      S. MacLane, Homology

Group cohomology

1.      K. Brown, Cohomology of groups

2.      L. Evens, Cohomology of groups

Triangulated categories

1.      A. Neeman, Triangulated categories

2.      S. Gel’fand, Yu. Manin, Methods of homological algebra

3.      M. Hovey, J. Palmieri, N. Strickland, Axiomatic stable homotopy theory

4.      P. May, The axioms for triangulated categories

Also useful: S. MacLane, Categories for the Working Mathematician

 

Homework:

·         Homework 1 .pdf, .tex

·         Homework 2 .pdf, .tex (due Wednesday, May 24)

 

Announcements:

There will be NO class on Monday, April 3rd. Please read about Abelian categories in chapter 1 of Weibel and do exercise 1.4.5 including optional 1.4.5.4.

 

Proof of the Snake Lemma