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 - Funding Information:
The authors would like to thank Cameron Gordon, Peter Kronheimer, Yankı Lekili, Tye Lidman, Robert Lipshitz, Peter Ozsváth, Sarah Rasmussen, Ivan Smith, Zoltan Szabó, and Claudius Zibrowius for helpful discussions, and the referee for their careful reading of the paper and many helpful suggestions. Part of this work was carried out while the third author was visiting Montréal as CIRGET research fellow, part was carried out while the second and third authors were participants in the program at the Isaac Newton Institute, and part while the third author was visiting the CRM as a Simons Visiting Professor. The authors would like to thank CIRGET, the CRM, and the Newton Institute for their support. JH was partially supported by NSF RTG grant DMS‐1148490; JR was partially supported by EPSRC grant EP/M000648/1; LW was partially supported by a Marie Curie career integration grant, by a Canada Research Chair, and by an NSERC discovery/accelerator grant; JR and LW were Isaac Newton Institute program participants while part of this work was completed and acknowledge partial support from EPSRC grant EP/K032208/1; additionally, LW was partially supported by a grant from the Simons Foundation while at the Isaac Newton Institute. Homology Theories in Low Dimensions
Funding Information:
The authors would like to thank Cameron Gordon, Peter Kronheimer, Yankı Lekili, Tye Lidman, Robert Lipshitz, Peter Ozsváth, Sarah Rasmussen, Ivan Smith, Zoltan Szabó, and Claudius Zibrowius for helpful discussions, and the referee for their careful reading of the paper and many helpful suggestions. Part of this work was carried out while the third author was visiting Montréal as CIRGET research fellow, part was carried out while the second and third authors were participants in the program Homology Theories in Low Dimensions at the Isaac Newton Institute, and part while the third author was visiting the CRM as a Simons Visiting Professor. The authors would like to thank CIRGET, the CRM, and the Newton Institute for their support. JH was partially supported by NSF RTG grant DMS-1148490; JR was partially supported by EPSRC grant EP/M000648/1; LW was partially supported by a Marie Curie career integration grant, by a Canada Research Chair, and by an NSERC discovery/accelerator grant; JR and LW were Isaac Newton Institute program participants while part of this work was completed and acknowledge partial support from EPSRC grant EP/K032208/1; additionally, LW was partially supported by a grant from the Simons Foundation while at the Isaac Newton Institute.
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 -