2018/10/22 by Hanselman, Jonathan, Rasmussen, Jacob, Watson, Liam · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1810.10355
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.