Work

Legendrian knots and monopoles

Year: 2006

Type: article

Abstract: We prove a generalization of Bennequin's inequality for Legendrian knots in a 3dimensional contact manifold .Y; /, 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 in [10] 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 .

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2006.6.1

Authors: Tomasz S Mrowka, Yann Rollin

Institutions: Massachusetts Institute of Technology, Imperial College London

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Basic Research in Mathematics