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On definite lattices bounded by a homology $3$–sphere and Yang–Mills instanton Floer theory

Christopher Scaduto

Geometry & Topology 28 (2024) 1587–1628
Abstract

Using instanton Floer theory, extending methods due to Frøyshov, we determine the definite lattices that arise from smooth 4–manifolds bounded by certain homology 3–spheres. For example, we show that for + 1 surgery on the (2,5) torus knot, the only nondiagonal lattices that can occur are E8 and the indecomposable unimodular definite lattice of rank 12, up to diagonal summands. We require that our 4–manifolds have no 2–torsion in their homology.

Keywords
instanton, Floer homology, 4–manifolds
Mathematical Subject Classification 2010
Primary: 57R57
Secondary: 57M99
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
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

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