Knot Theory and Grid Homology

Department: 
Math
Course Number: 
4803-HOM
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
3
Hours - Total Credit: 
3
Typical Scheduling: 
Not regularly scheduled

Special topics course offered in Spring 2020 by Jennifer Hom.

Prerequisites: 

Math 1564 (Linear Algebra with Abstract Vector Spaces) or Math 2106 (Foundations of Mathematical Proof).

Course Text: 

Peter S. Ozsvath, Andras I. Stipsicz, and Zoltan Szabo  ``Grid homology for knots and links'' available online at https://web.math.princeton.edu/~petero/GridHomologyBook.pdf

Topic Outline: 
  • Introduction to knot theory: knots and links, Seifert surfaces, signature, unknotting number, knot group, Alexander polynomial, grid diagrams
  • Introduction to homological algebra: modules, chain complexes, homology, mapping cones
  • Grid homology: definition, invariance, basic properties and applications