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A characterization of heaviness in terms of relative symplectic cohomology

A characterization of heaviness in terms of relative symplectic cohomology
A characterization of heaviness in terms of relative symplectic cohomology
For a compact subset K of a closed symplectic manifold (M, ω), we prove that K is heavy if and only if its relative symplectic cohomology over the Novikov field is non-zero. As an application we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results are also included.
1753-8416
Mak, Cheuk Yu
49c234b8-842f-4cda-b082-d36505c24626
Sun, Yuhan
467fdd59-6169-4ace-a994-85cb86c58276
Varolgunes, Umut
c617015d-85e4-45e4-b385-d1c567c1b613
Mak, Cheuk Yu
49c234b8-842f-4cda-b082-d36505c24626
Sun, Yuhan
467fdd59-6169-4ace-a994-85cb86c58276
Varolgunes, Umut
c617015d-85e4-45e4-b385-d1c567c1b613

Mak, Cheuk Yu, Sun, Yuhan and Varolgunes, Umut (2024) A characterization of heaviness in terms of relative symplectic cohomology. Journal of Topology, 17 (1), [e12327]. (doi:10.1112/topo.12327).

Record type: Article

Abstract

For a compact subset K of a closed symplectic manifold (M, ω), we prove that K is heavy if and only if its relative symplectic cohomology over the Novikov field is non-zero. As an application we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results are also included.

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2301.12625 - Accepted Manuscript
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Accepted/In Press date: 2 February 2024
e-pub ahead of print date: 9 March 2024
Published date: March 2024
Additional Information: Publisher Copyright: © 2024 The Authors. Journal of Topology is copyright © London Mathematical Society.

Identifiers

Local EPrints ID: 486787
URI: http://eprints.soton.ac.uk/id/eprint/486787
ISSN: 1753-8416
PURE UUID: 875a9ef5-f859-4c76-8cdc-8138471957ab
ORCID for Cheuk Yu Mak: ORCID iD orcid.org/0000-0001-6334-7114

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Date deposited: 06 Feb 2024 17:38
Last modified: 30 May 2024 02:04

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Contributors

Author: Cheuk Yu Mak ORCID iD
Author: Yuhan Sun
Author: Umut Varolgunes

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