Volume 20, issue 2 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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.

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