Comparing homological invariants for mapping classes of surfaces
Abstract
We compare two different types of mapping class invariants: the Hochschild homology of an bimodule coming from bordered Heegaard Floer homology, and fixed point Floer cohomology. We first compute the bimodule invariants and their Hochschild homology in the genus two case. We then compare the resulting computations to fixed point Floer cohomology, and make a conjecture that the two invariants are isomorphic. We also discuss a construction of a map potentially giving the isomorphism. It comes as an open-closed map in the context of a surface being viewed as a -dimensional Lefschetz fibration over the complex plane.
Keywords
Cite
@article{arxiv.1702.04071,
title = {Comparing homological invariants for mapping classes of surfaces},
author = {Artem Kotelskiy},
journal= {arXiv preprint arXiv:1702.04071},
year = {2020}
}
Comments
Major revision; changes include the overall structure and improved usability of the computer program. Final version, to appear in Michigan Mathematical journal