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.

Keywords
homology $3$–sphere, $4$–manifold, gauge theory, Chern–Simons functional
Mathematical Subject Classification 2010
Primary: 57M25, 57M27