MA 753: Algebraic Topology (Spring 2018)

Instructor:  Tye Lidman
E-mail: tlid 'at' math 'dot' ncsu 'dot' edu
Office: SAS 3246
Office Hours: TBD
Course Location: 532 Poe Hall
Course Time: TuTh 11:45AM-1:00PM

Course Syllabus


Lectures:
Overview, more fundamental group (1/9)
Intro to covering spaces (1/11)
Lifting criteria (1/16)
Universal covers (1/23)
Characterizing covering spaces (1/25)
Group actions as covers (1/30)
Deck transformations (2/1)
Intro to homology (2/6)
Chain maps and graph homology (2/8)
More homological algebra (2/13)
The snake lemma (2/15)
Simplicial and singular homology (2/20)
More on singular homology (2/22)
The long exact sequence for a pair (3/1)
Naturality, excision, and facts about homology (3/13)
Degrees of maps (3/15)
Cellular homology (3/22)
More cellular homology (3/27)
Mayer-Vietoris (3/29)
Tensor products and coefficients (4/3)
Categories and functors (4/5)
Fundamental group and homology (4/10)
Cohomology (4/12)
More cohomology (4/17)
Cup products (4/19)



Homework:
Homework 1 (Due 1/18)
Homework 2 (Due 2/1)
Homework 3 (Due 2/8)
Homework 4 (Due 2/15)
Homework 5 (Due 2/22)
Homework 6 (Due 3/1)
Homework 7 (Due 3/15)
Homework 8 (Due 3/29)
Homework 9 (Due 4/5)
Homework 10 (Due 4/12)
Homework 11 (Due 4/19)
Homework 12 (Due 4/26)