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Legendrian knots and monopoles

Tomasz S Mrowka·Yann Rollin
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Abstract

We prove a generalization of Bennequin's inequality for Legendrian knots in a 3-dimensional contact manifold (Y,xi), 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. 2009-02-20. Legendrian knots and monopoles. https://doi.org/10.2140/agt.2006.6.1

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