Heegaard Floer homology for manifolds with torus boundary: properties and examples
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Authors
Hanselman, Jonathan
Rasmussen, Jacob
Watson, Liam
Journal Title
Proceedings of the London Mathematical Society
ISSN
0024-6115
Publisher
London Mathematical Society
Type
Article
This Version
AM
Metadata
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Hanselman, J., Rasmussen, J., & Watson, L. Heegaard Floer homology for manifolds with torus boundary: properties
and examples. Proceedings of the London Mathematical Society https://doi.org/10.17863/CAM.86271
Abstract
This is a companion paper to earlier work of the authors, which interprets
the Heegaard Floer homology for a manifold with torus boundary in terms of
immersed curves in a punctured torus. We prove 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 spin$^c$ 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 $HF^\pm$. Many examples are
included.
Keywords
math.GT, math.GT
Sponsorship
Engineering and Physical Sciences Research Council (EP/M000648/1)
Embargo Lift Date
2025-07-06
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.86271
This record's URL: https://www.repository.cam.ac.uk/handle/1810/338865
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