Geodesic
Monopoles and lens space surgeries
Peter Kronheimer1 ; Tomasz Mrowka2 ; Peter Ozsváth3 ; Zoltán Szabó4
1 Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
3 Department of Mathematics, Columbia University, New York, NY 10027, United States
4 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
Annals of mathematics, Tome 165 (2007) no. 2, pp. 457-546.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a nontrivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer homology, together with a nonvanishing theorem, which shows that monopole Floer homology detects the unknot. In addition, we apply these techniques to give information about knots which admit lens space surgeries, and to exhibit families of three-manifolds which do not admit taut foliations.
DOI : 10.4007/annals.2007.165.457

Peter Kronheimer 1 ; Tomasz Mrowka 2 ; Peter Ozsváth 3 ; Zoltán Szabó 4

1 Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
3 Department of Mathematics, Columbia University, New York, NY 10027, United States
4 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States 
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Peter Kronheimer; Tomasz Mrowka; Peter Ozsváth; Zoltán Szabó. Monopoles and lens space surgeries. Annals of mathematics, Tome 165 (2007) no. 2, pp. 457-546. doi : 10.4007/annals.2007.165.457. http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.165.457/

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