Algebraic torsion via Heegaard Floer homology
Cagatay Kutluhan, Gordana Matic, Jeremy Van Horn-Morris, Andy Wand
TL;DR
This paper explores the algebraic torsion concept within Heegaard Floer homology, adapting Hutchings's ECH-based approach to establish connections with Seiberg-Witten Floer homologies.
Contribution
It provides a translation of Hutchings's algebraic torsion from embedded contact homology to Heegaard Floer homology, enhancing understanding of their relationship.
Findings
Establishes an ECH analog of algebraic k-torsion in Heegaard Floer homology
Clarifies the translation of algebraic torsion concepts between ECH and Heegaard Floer homology
Supports the isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies
Abstract
We outline Hutchings's prescription that produces an ECH analog of Latschev and Wendl's algebraic -torsion in the context of , a variant of ECH used in a proof of the isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies; and we explain how it translates into Heegaard Floer homology.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Homotopy and Cohomology in Algebraic Topology