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Rational homology
$3$–spheres and simply connected definite bounding
Kouki Sato and Masaki Taniguchi |
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Algebraic & Geometric Topology 20 (2020) 865–882
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Abstract |
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For each rational homology –sphere which bounds simply connected definite –manifolds of both signs, we construct an infinite family of irreducible rational homology –spheres which are homology cobordant to but cannot bound any simply connected definite –manifold. As a corollary, for any coprime integers and , we obtain an infinite family of irreducible rational homology –spheres which are homology cobordant to the lens space but cannot be obtained by a knot surgery. |
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Keywords
homology $3$–sphere, $4$–manifold, gauge theory,
Chern–Simons functional
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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References |
Publication
Received: 21 October 2018
Revised: 27 July 2019
Accepted: 22 August 2019
Published: 23 April 2020
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Authors |
| Kouki Sato | |
| Graduate School of Mathematical
Sciences University of Tokyo Meguro Japan |
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| Masaki Taniguchi | |
| Graduate School of Mathematical
Sciences University of Tokyo Meguro Japan |
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