Introduction to Heegaard Floer homology

Department: 
MATH
Course Number: 
8803-HOM
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Not regularly scheduled

Special topics course on Introduction to Heegaard Floer homology offered in Fall 2017 by Jennifer Hom.

Prerequisites: 

MATH 6441, Algebraic Topology I

Course Text: 

TBA

Topic Outline: 

Heegaard Floer homology, defined by Ozsvath and Szabo in the early
2000s, has proved to be a powerful tool in low-dimensional topology. We
will begin by defining Heegaard Floer homology, and then move on to the
following topics:

- Grid diagrams and combinatorial knot Floer homology
- Applications to the knot concordance and homology cobordism groups
- Applications to contact geometry and Legendrian knot theory
- Surgery formulas
- Bordered Floer homology for manifolds with boundary
- Computations by factoring mapping class groups