Volume 6, issue 1 (2006)

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

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

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
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