Volume 6, issue 1 (2006)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Legendrian knots and monopoles

Tomasz S Mrowka and Yann Rollin

Algebraic & Geometric Topology 6 (2006) 1–69

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