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On
definite lattices bounded by a homology $3$–sphere and
Yang–Mills instanton Floer theory
Christopher Scaduto |
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Geometry & Topology 28 (2024) 1587–1628
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Abstract |
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Using instanton Floer theory, extending methods due to Frøyshov, we determine the definite lattices that arise from smooth –manifolds bounded by certain homology –spheres. For example, we show that for surgery on the (2,5) torus knot, the only nondiagonal lattices that can occur are and the indecomposable unimodular definite lattice of rank 12, up to diagonal summands. We require that our –manifolds have no –torsion in their homology. |
Keywords
instanton, Floer homology, 4–manifolds
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Mathematical Subject Classification 2010
Primary: 57R57
Secondary: 57M99
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References |
Publication
Received: 21 February 2019
Revised: 3 February 2021
Accepted: 22 October 2022
Published: 18 July 2024
Proposed: Peter Teichner
Seconded: Paul Seidel, Tomasz S Mrowka
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Authors |
| Christopher Scaduto | |
| Simons Center for Geometry and
Physics Stony Brook University Stony Brook, NY United States |
Department of Mathematics University of Miami Coral Gables, FL United States |
| https://www.math.miami.edu/~cscaduto/index.html | |
| © 2024 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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