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Symplectic excision
Yael Karshon and Xiudi Tang |
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Geometry & Topology 30 (2026) 2217–2249
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Abstract |
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We use time-independent incomplete Hamiltonian flows to excise interesting closed subsets of positive codimension from symplectic manifolds. Examples of such subsets include what we call a “Cantor brush”, a “box with a tail”, and, more generally, epigraphs of lower semicontinuous functions. This answers a question of Alan Weinstein about excision of a ray, and it generalizes a result of Bernd Stratmann about excision of the product of a ray with a manifold. |
Keywords
symplectic geometry, symplectic excision,
symplectomorphism, incomplete vector field, Hamiltonian
flow
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Mathematical Subject Classification
Primary: 53D05
Secondary: 37J39, 53D35
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References |
Publication
Received: 7 August 2024
Revised: 21 December 2025
Accepted: 30 January 2026
Published: 31 July 2026
Proposed: Yakov Eliashberg
Seconded: Jianfeng Lin, Robert Lipshitz
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Authors |
| Yael Karshon | |
| School of Mathematical
Sciences Tel-Aviv University Tel Aviv Israel |
Department of Mathematics University of Toronto Toronto, ON Canada |
| Xiudi Tang | |
| School of Mathematics and
Statistics Beijing Institute of Technology Beijing China |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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