**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outdated, this is a classic where the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 2 .pdf, .tex (due Wednesday, May 24)

**Announcements:**

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