Special topics course on Introduction to Heegaard Floer homology offered in Fall 2017 by Jennifer Hom.
MATH 6441, Algebraic Topology I
TBA
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