MA 591 - Algebraic
Topology and Homological Algebra

Instructor:
Tye Lidman

E-mail: tlid
`at' math `dot' ncsu `dot' edu

Office: SAS
3246

Office Hours: M 12:30-1:30, 2:45-3:45

Course Location: SAS
2106

Course Time: MW
1:30-2:45

Course Syllabus

Homework:

Homework 1 (Due 2/17)

Homework 2 (Due 3/20)

Expository Writing Assignment: (details)

Topic Choice (Due 3/13)

Submit Article (Due 4/10)

Lectures:

Review of Homological Algebra (1/11, 1/18)

Introduction to Cohomology (1/23)

A categorical viewpoint (1/25)

Exact sequences in cohomology (1/30, 2/1)

The cup product on singular cohomology (2/1, 2/6)

Free resolutions of modules (2/8)

Tor and Ext (2/13)

Introduction to group cohomology (2/15, 2/20)

More on group cohomology (2/20, 2/22, 2/27)

Group cohomology and extensions (3/1)

Universal Coefficients and Kunneth Formula (3/8, 3/15)

Manifolds, orientability, and homology (3/15, 3/20, 3/22)

Poincare Duality (3/22, 3/27)

Proof of Poincare Duality (3/29)

Other duality theorems (3/29, 4/3)

Higher homotopy groups (4/3)

Relative homotopy and exact sequences (4/5)

Whitehead's Theorem (4/10)

Freudenthal suspension Theorem (4/10)

Hurewicz Theorem (4/12)

Fibrations (4/12, 4/17)