2023/10/12 by Antonio Alfieri, Alfieri, Antonio, Alberto Cavallo +1 · 1 citation
Mathematics · #57K18 #57K33 #57K43 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2310.08657
openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The scope of the paper is threefold. First, we build on recent work by Hayden to compute Hedden's tau-invariant τξ(L) in the case when ξ is a Stein fillable contact structure on a rational homology sphere, and L is a transverse link arising as the boundary of a pseudo-holomorphic curve. This leads to a new proof of the relative Thom conjecture for Stein domains. Secondly, we compare the invariant τξ to the Grigsby-Ruberman-Strle topological tau-invariant τ\mathfrak s, associated to the Spinc-structure \mathfrak s=\mathfrak sξ of the contact structure ξ, to obtain topological obstructions for a link type to admit a holomorphically fillable transverse representative. Finally, we use our main result together with methods from lattice cohomology to compute the τ\mathfrak s-invariants of certain links in lens spaces, and estimate their PL slice genus.