Mak, C.Y. orcid.org/0000-0001-6334-7114 and Trifa, I. (2025) Hameomorphism groups of positive genus surfaces. Commentarii Mathematici Helvetici: A Journal of the Swiss Mathematical Society. ISSN 0010-2571
Abstract
In their 2021 and 2022 papers, Cristofaro-Gardiner, Humilière, Mak, Seyfaddini, and Smith defined links spectral invariants on connected compact surfaces and used them to show various results on the algebraic structure of the group of area-preserving homeomorphisms of surfaces, particularly in cases where the surfaces have genus zero. We show that on surfaces with higher genus, for a certain class of links, the invariants will satisfy a local quasimorphism property. Subsequently, we generalize their results to surfaces of any genus. This extension includes the non-simplicity of (i) the group of hameomorphisms of a closed surface, and (ii) the kernel of the Calabi homomorphism inside the group of hameomorphisms of a surface with non-empty boundary. Moreover, we prove that the Calabi homomorphism extends (non-canonically) to the C0-closure of the set of Hamiltonian diffeomorphisms of any surface. The local quasimorphism property is a consequence of a quantitative Künneth formula for a connected sum in Heegaard–Floer homology, inspired by the results of Ozsváth and Szabó.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in Commentarii Mathematici Helvetici: A Journal of the Swiss Mathematical Society is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ |
Keywords: | spectral invariants; Floer homology; local quasimorphisms |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Funding Information: | Funder Grant number Royal Society URF\R1\221047 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Jan 2025 14:39 |
Last Modified: | 06 Jun 2025 15:59 |
Status: | Published online |
Publisher: | EMS Press |
Refereed: | Yes |
Identification Number: | 10.4171/cmh/601 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221327 |
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Licence: CC-BY 4.0