Rational homology 3–spheres and simply connected definite bounding

Sato, Kouki; Taniguchi, Masaki

doi:10.2140/agt.2020.20.865

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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

DOI: 10.2140/agt.2020.20.865

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.

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

Volume 20, issue 2 (2020)