2025/06/08 by Antonio Alfieri, Alfieri, Antonio, Chi Cheuk Tsang +1
Mathematics · #Advanced Combinatorial Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2506.07163
openalex publication_date 2025/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In earlier work, relying on work of Agol-Guéritaud and Landry-Minsky-Taylor, we showed that given a pseudo-Anosov flow (Y,ϕ) and a collection of closed orbits C satisfying the `no perfect fit' condition, one can construct a special Heegaard diagram for the link complement Y^\sharp= Y ∖ ν(C) framed by the degeneracy curves. In this paper, we demonstrate how the special combinatorics of this diagram can be used to understand the differential of the associated Heegaard Floer chain complex. More specifically, we introduce a refinement of the spinc-grading obstructing two Heegaard states from being connected by an effective domain. We describe explicitly the subcomplexes in the refined gradings that represent irreducible multi-orbits, in the sense that they contain states corresponding to multi-orbits which cannot be resolved along Fried pants. In particular we show that the homology of these subcomplexes are 1-dimensional. When specialized to the case of suspension flows our arguments prove some results in the spirit of Ni, Ghiggini, and Spano: the next-to-top non-zero sutured Floer group counts the number of periodic points of least period.