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2006 Legendrian knots and monopoles
Tomasz S Mrowka, Yann Rollin
Algebr. Geom. Topol. 6(1): 1-69 (2006). DOI: 10.2140/agt.2006.6.1

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.

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Tomasz S Mrowka. Yann Rollin. "Legendrian knots and monopoles." Algebr. Geom. Topol. 6 (1) 1 - 69, 2006. https://doi.org/10.2140/agt.2006.6.1

Information

Received: 8 November 2005; Accepted: 10 July 2005; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1207.57015
MathSciNet: MR2199446
Digital Object Identifier: 10.2140/agt.2006.6.1

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

Rights: Copyright © 2006 Mathematical Sciences Publishers

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