Steven Sivek: A contact invariant in sutured monopole homology

Kronheimer and Mrowka recently used monopole Floer homology to define an invariant of sutured manifolds, following work of Juhász in Heegaard Floer homology. Contact 3-manifolds with boundary are natural examples of such manifolds. In this talk, I will construct an invariant of a contact structure as an element of the associated sutured monopole homology group. I will discuss several interesting properties of this invariant, including gluing maps which are analogous to the Heegaard Floer sutured gluing maps of Honda, Kazez, and Matic, and a bypass exact triangle relating the homology groups for different choices of sutures. This is joint work with John Baldwin.

Steven Sivek
Harvard University