TY - JOUR
T1 - Monopoles and lens space surgeries
AU - Kronheimer, P.
AU - Mrowka, T.
AU - Ozsváth, P.
AU - Szabó, Z.
PY - 2007/3
Y1 - 2007/3
N2 - 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.
AB - 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.
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U2 - 10.4007/annals.2007.165.457
DO - 10.4007/annals.2007.165.457
M3 - Article
AN - SCOPUS:34247490022
SN - 0003-486X
VL - 165
SP - 457
EP - 546
JO - Annals of Mathematics
JF - Annals of Mathematics
IS - 2
ER -