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)