Legendrian knots and monopoles

Mrowka, Tomasz S; Rollin, Yann

doi:10.2140/agt.2006.6.1

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Legendrian knots and monopoles

Tomasz S Mrowka and Yann Rollin

Algebraic & Geometric Topology 6 (2006) 1–69

DOI: 10.2140/agt.2006.6.1

arXiv: math.DG/0410559

Abstract

We prove a generalization of Bennequin’s inequality for Legendrian knots in a 3-dimensional contact manifold $(Y, ξ)$ , under the assumption that $Y$ is the boundary of a 4-dimensional manifold $M$ and the version of Seiberg-Witten invariants introduced by Kronheimer and Mrowka [Invent. Math. 130 (1997) 209–255] is nonvanishing. The proof requires an excision result for Seiberg-Witten moduli spaces; then the Bennequin inequality becomes a special case of the adjunction inequality for surfaces lying inside $M$ .

Keywords

contact structures, Legendrian knots, Bennequin inequality, excision, monopoles

Mathematical Subject Classification 2000

Primary: 57R17, 57M25, 57M27, 57R57

References

Forward citations

Publication

Received: 8 November 2005

Accepted: 10 July 2005

Published: 24 February 2006

Authors

Tomasz S Mrowka
MIT 77 Massachusetts Avenue Cambridge MA 02139 USA

Yann Rollin
Imperial College Huxley Building 180 Queen’s Gate London SW7 2AZ UK

Volume 6, issue 1 (2006)