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(p,q) 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
References
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