Geodesic
Legendrian knots and monopoles
Mrowka, Tomasz S1 ; Rollin, Yann2
1MIT, 77 Massachusetts Avenue, Cambridge MA 02139, USA
2Imperial College, Huxley Building, 180 Queen’s Gate, London SW7 2AZ, UK
Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 1-69
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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.

DOI : 10.2140/agt.2006.6.1
Keywords: contact structures, Legendrian knots, Bennequin inequality, excision, monopoles

Mrowka, Tomasz S  1   ; Rollin, Yann  2

1 MIT, 77 Massachusetts Avenue, Cambridge MA 02139, USA
2 Imperial College, Huxley Building, 180 Queen’s Gate, London SW7 2AZ, UK 
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Mrowka, Tomasz S; Rollin, Yann. Legendrian knots and monopoles. Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 1-69. doi: 10.2140/agt.2006.6.1

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