#### Volume 20, issue 2 (2020)

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Rational homology $3$–spheres and simply connected definite bounding

### Kouki Sato and Masaki Taniguchi

Algebraic & Geometric Topology 20 (2020) 865–882
##### Abstract

For each rational homology $3$–sphere $Y$ which bounds simply connected definite $4$–manifolds of both signs, we construct an infinite family of irreducible rational homology $3$–spheres which are homology cobordant to $Y$ but cannot bound any simply connected definite $4$–manifold. As a corollary, for any coprime integers $p$ and $q$, we obtain an infinite family of irreducible rational homology $3$–spheres which are homology cobordant to the lens space $L\left(p,q\right)$ but cannot be obtained by a knot surgery.

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##### Keywords
homology $3$–sphere, $4$–manifold, gauge theory, Chern–Simons functional
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
##### Publication
Received: 21 October 2018
Revised: 27 July 2019
Accepted: 22 August 2019
Published: 23 April 2020
##### Authors
 Kouki Sato Graduate School of Mathematical Sciences University of Tokyo Meguro Japan Masaki Taniguchi Graduate School of Mathematical Sciences University of Tokyo Meguro Japan