dc.contributor.author
Cardona, Robert
dc.contributor.author
Gironella, F.
dc.date.accessioned
2025-06-16T08:27:40Z
dc.date.available
2025-06-16T08:27:40Z
dc.date.issued
2025-04-04
dc.identifier.uri
http://hdl.handle.net/2072/484445
dc.description.abstract
We push forward the study of higher dimensional stable Hamiltonian topology by establishing two nondensity results. First, we prove that stable hypersurfaces are not (Formula presented.) -dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension (Formula presented.). Our second result is that on any manifold of dimension (Formula presented.), the set of non-degenerate stable Hamiltonian structures is not (Formula presented.) -dense among stable Hamiltonian structures in any given stable homotopy class that satisfies a mild assumption. The latter generalizes a result by Cieliebak and Volkov to arbitrary dimensions.
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dc.description.sponsorship
Robert Cardona acknowledges partial support from the AEI grant PID2023-147585NA-I00, the Departament de Recerca i Universitats de la Generalitat de Catalunya (2021 SGR 00697), and the Spanish State Research Agency, through the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M). Fabio Gironella benefits from the support of the ANR Grant COSY \u201CNew challenges in symplectic and contact topology,\u201D bearing the reference ANR-21-CE40-0002; of the region Pays de la Loire, via the project \u00C9toile Montante 2023 SymFol; and of the French government's \u201CInvestissements d'Avenir\u201D program integrated to France 2030, bearing the following reference ANR-11-LABX-0020-01.; Funding text 2: The authors are grateful to Jonathan Bowden for his suggestions to prove Theorem 17 , and to Viktor Ginzburg for explaining them in detail an argument in [ 25 , Lemma 3.4] that is needed for the proof of Proposition 18 . Robert Cardona acknowledges partial support from the AEI grant PID2023\u2010147585NA\u2010I00, the Departament de Recerca i Universitats de la Generalitat de Catalunya (2021 SGR 00697), and the Spanish State Research Agency, through the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020\u2010001084\u2010M). Fabio Gironella benefits from the support of the ANR Grant COSY \u201CNew challenges in symplectic and contact topology,\u201D bearing the reference ANR\u201021\u2010CE40\u20100002; of the region Pays de la Loire, via the project \u00C9toile Montante 2023 SymFol; and of the French government's \u201CInvestissements d'Avenir\u201D program integrated to France 2030, bearing the following reference ANR\u201011\u2010LABX\u20100020\u201001.
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dc.format.extent
25 p.
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dc.publisher
John Wiley and Sons
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dc.relation.ispartof
Journal of the London Mathematical Society
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dc.rights
© 2025 The Author(s).
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dc.rights
Attribution 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Symplectic and contact topology
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dc.title
Nondensity results in high-dimensional stable Hamiltonian topology
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1112/jlms.70143
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
