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)