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September 26, 2025Journal of the European Mathematical Society0 citationsOpen Access

Sutured Heegaard Floer and embedded contact homologies are isomorphic

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VCVincent ColinPGPaolo GhigginiKHKo Honda

Key Points

  • The equivalence of sutured Heegaard Floer homology and embedded contact homology was established, unlocking new theoretical connections.
  • This study shows that the knot versions of Heegaard Floer homology and embedded contact homology are equivalent, revealing deeper structural insights.
  • The analysis indicates that product sutured 3-manifolds are characterized by an adapted Reeb vector field lacking periodic orbits.
  • By proving these equivalences, we advance the understanding of sutured and monopole Floer homologies in the context of contact geometry.

Abstract

We prove the equivalence of the sutured versions of Heegaard Floer homology, monopole Floer homology, and embedded contact homology. As applications we show that the knot versions of Heegaard Floer homology and embedded contact homology are equivalent and that product sutured 3 -manifolds are characterized by the fact that they carry an adapted Reeb vector field without periodic orbits.

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Cite This Study

Colin et al. (2025) studied this question.

synapsesocial.com/papers/68d6c682b1249cec298b28e1https://doi.org/10.4171/jems/1719
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