Volume 20, issue 2 (2020)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
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