TY - JOUR

T1 - Heegaard Floer homology for manifolds with torus boundary

T2 - properties and examples

AU - Hanselman, Jonathan

AU - Rasmussen, Jacob

AU - Watson, Liam

N1 - Publisher Copyright:
© 2022 The Authors. Proceedings of the London Mathematical Society is copyright © London Mathematical Society.

PY - 2022/10

Y1 - 2022/10

N2 - This is a companion paper to earlier work of the authors (Preprint, arXiv:1604.03466, 2016), which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We establish a variety of properties of this invariant, paying particular attention to its relation to knot Floer homology, the Thurston norm, and the Turaev torsion. We also give a geometric description of the gradings package from bordered Heegaard Floer homology and establish a symmetry under (Formula presented.) conjugation; this symmetry gives rise to genus one mutation invariance in Heegaard Floer homology for closed three-manifolds. Finally, we include more speculative discussions on relationships with Seiberg–Witten theory, Khovanov homology, and (Formula presented.). Many examples are included.

AB - This is a companion paper to earlier work of the authors (Preprint, arXiv:1604.03466, 2016), which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We establish a variety of properties of this invariant, paying particular attention to its relation to knot Floer homology, the Thurston norm, and the Turaev torsion. We also give a geometric description of the gradings package from bordered Heegaard Floer homology and establish a symmetry under (Formula presented.) conjugation; this symmetry gives rise to genus one mutation invariance in Heegaard Floer homology for closed three-manifolds. Finally, we include more speculative discussions on relationships with Seiberg–Witten theory, Khovanov homology, and (Formula presented.). Many examples are included.

UR - http://www.scopus.com/inward/record.url?scp=85137446658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85137446658&partnerID=8YFLogxK

U2 - 10.1112/plms.12473

DO - 10.1112/plms.12473

M3 - Article

C2 - 36632360

AN - SCOPUS:85137446658

SN - 0024-6115

VL - 125

SP - 879

EP - 967

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 4

ER -