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Heegaard Floer homology for manifolds with torus boundary: properties and examples.

Published version
Peer-reviewed

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Authors

Hanselman, Jonathan 
Rasmussen, Jacob 
Watson, Liam 

Abstract

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 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 ± . Many examples are included.

Description

Funder: CIRGET


Funder: CRM; Id: http://dx.doi.org/10.13039/100013509


Funder: Marie Curie; Id: http://dx.doi.org/10.13039/501100000654


Funder: Canada Research Chair


Funder: NSERC; Id: http://dx.doi.org/10.13039/501100000038

Keywords

math.GT, math.GT

Journal Title

Proc Lond Math Soc

Conference Name

Journal ISSN

0024-6115
1460-244X

Volume Title

Publisher

Wiley
Sponsorship
Engineering and Physical Sciences Research Council (EP/M000648/1)
Engineering and Physical Sciences Research Council (EP/K032208/1)