Holomorphic disks and three-manifold invariants: Properties and applications

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Abstract

In [27], we introduced Floer homology theories HF-(Y, s)t HF(Y,s), HF+(Y,t), HF(Y,s),and. HF red(Y,s) associated to closed, oriented three-manifolds Y equipped with a Spinc structures s ∈ Spinc(Y). In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory. The properties include a relationship between the Euler characteristics of HF ± and Turaev's torsion, a relationship with the minimal genus problem (Thurston norm), and surgery exact sequences. We also include some applications of these techniques to three-manifold topology.

Original languageEnglish (US)
Pages (from-to)1159-1245
Number of pages87
JournalAnnals of Mathematics
Volume159
Issue number3
DOIs
StatePublished - May 2004

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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