Sutured Heegaard Floer and embedded contact homologies are isomorphic

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.