Witten’s conjecture and Property P

Kronheimer, Peter B; Mrowka, Tomasz S

doi:10.2140/gt.2004.8.295

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Witten's conjecture and Property P

Peter B Kronheimer and Tomasz S Mrowka

Geometry & Topology 8 (2004) 295–310

DOI: 10.2140/gt.2004.8.295

arXiv: math.GT/0311489

Abstract

Let $K$ be a non-trivial knot in the $3$ –sphere and let $Y$ be the $3$ –manifold obtained by surgery on $K$ with surgery-coefficient $1$ . Using tools from gauge theory and symplectic topology, it is shown that the fundamental group of $Y$ admits a non-trivial homomorphism to the group $S O (3)$ . In particular, $Y$ cannot be a homotopy-sphere.

Keywords

3–manifold, knot, surgery, homotopy sphere, gauge theory

Mathematical Subject Classification 2000

Primary: 57M25, 57R57

Secondary: 57R17

References

Forward citations

Publication

Received: 7 December 2003

Revised: 9 December 2003

Accepted: 13 February 2004

Published: 14 February 2004

Proposed: Robion Kirby

Seconded: John Morgan, Ronald Stern

Authors

Peter B Kronheimer
Department of Mathematics Harvard University Cambridge Massachusetts 02138 USA

Tomasz S Mrowka
Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA

Volume 8, issue 1 (2004)