Monopoles and lens space surgeries

Abstract

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a non-trivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer homology, together with a non-vanishing 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.

Corrected typeos and references

References in corpus (6)

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• On the Floer homology of plumbed three-manifolds
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• Holomorphic disks and knot invariants
• (-2,3,7)-pretzel knot and Reebless foliation
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Cited by in corpus (10)

• Lens space surgeries and L-space homology spheres
• Dehn surgery, the fundamental group and SU(2)
• Tight contact structures and genus one fibered knots
• Lectures on Contact Geometry in Low-Dimensional Topology
• Surfaces in 4-manifolds: Addendum
• Knot Floer homology detects genus-one fibred knots
• Geometric and algebraic presentations of Weinstein domains
• Knots with unknotting number one and Heegaard Floer homology
• Lens spaces given from L-space homology 3-spheres
• Alexander polynomials of doubly primitive knots