Volume 8 (2006)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Lagrangians for the Gopakumar–Vafa conjecture

Clifford Henry Taubes

Geometry & Topology Monographs 8 (2006) 73–95

DOI: 10.2140/gtm.2006.8.73

arXiv: math.DG/0201219

Abstract

This article explains how to construct immersed Lagrangian submanifolds in C2 that are asymptotic at large distance from the origin to a given braid in the 3–sphere. The self-intersections of the Lagrangians are related to the crossings of the braid. These Lagrangians are then used to construct immersed Lagrangians in the vector bundle O(-1)⊕O(-1) over the Riemann sphere which are asymptotic at large distance from the zero section to braids.

Reproduced by kind permission of International Press from: Advances in Theoretical and Mathematical Physics 5 (2002) 139–163

Keywords

Lagrangian submanifolds, braids, large N duality

Mathematical Subject Classification

Primary: 53D45

Secondary: 53D12, 57M27

References
Publication

Received: 22 January 2002
Published: 22 April 2006

Authors
Clifford Henry Taubes
Department of Mathematics
Harvard University
Cambridge
Massachusetts 02138
USA