Heegaard Floer homology for manifolds with torus boundary: properties and examples. Issue 4 (8th September 2022)

• Record Type: Journal Article
• Authors: Hanselman, Jonathan; Rasmussen, Jacob; Watson, Liam
• Is Part Of: Proceedings of the London Mathematical Society. Volume 125:Issue 4(2022)
• Page Start: 879
• Page End: 967
• Publication Date: 2022-09-08
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12473
• Languages: English
• ISSNs: 0024-6115

Abstract

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 $\operatorname{Spin}^c$ 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 ± $\mathit {HF}^\pm$ . Many examples are included.