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August 2021 Comparing Homological Invariants for Mapping Classes of Surfaces
Artem Kotelskiy
Michigan Math. J. 70(3): 503-560 (August 2021). DOI: 10.1307/mmj/1599271513

Abstract

We compare two different types of mapping class invariants: the Hochschild homology of an A 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 viewed as a 0-dimensional Lefschetz fibration over the complex plane.

Citation

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Artem Kotelskiy. "Comparing Homological Invariants for Mapping Classes of Surfaces." Michigan Math. J. 70 (3) 503 - 560, August 2021. https://doi.org/10.1307/mmj/1599271513

Information

Received: 13 November 2017; Revised: 26 May 2020; Published: August 2021
First available in Project Euclid: 5 September 2020

Digital Object Identifier: 10.1307/mmj/1599271513

Subjects:
Primary: 53D37, 57K20, 57K31, 57R58

Rights: Copyright © 2021 The University of Michigan

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Vol.70 • No. 3 • August 2021
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