2018/10/22 by Jonathan Hanselman, Jacob Rasmussen, Hanselman, Jonathan +3 · 6 citations
Mathematics · Medicine · #Algebra over a field #Anatomy #Botulinum Toxin and Related Neurological Disorders #Cellular homology #FOS: Mathematics #Fibered knot #Floer homology #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Heegaard splitting #Homology (biology) #Invariant (physics) #Khovanov homology #Knot (papermaking) #Mathematical physics #Mathematics #Morse homology #Pure mathematics #Symplectic geometry #Torsion (gastropod) #Torus #math.GT
paper · pdf · doi:10.48550/arxiv.1810.10355
published in arXiv (Cornell University) (Cornell University) · 73 pages, 66 figures. arXiv admin note: text overlap with arXiv:1604.03466
arxiv created 2018/10/22 · openalex publication_date 2018/10/22 · arxiv updated 2018/10/25 · openalex created_date 2022/09/09 · openalex updated_date 2026/08/06
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 spinc 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.