2021/11/14 by Hans Bodén, Hans U. Boden, Boden, Hans U. +2
Mathematics · Medicine · #57K10 #57K12 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57K10 #msc:57K12
paper · pdf · doi:10.48550/arxiv.2111.07409
24 pages, 5 figures, comments welcome
arxiv created 2021/11/14 · openalex publication_date 2021/11/14 · arxiv updated 2021/11/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Using the Gordon-Litherland pairing, one can define invariants (signature, nullity, determinant) for \mathbb Z/2 null-homologous links in thickened surfaces. In this paper, we study the concordance properties of these invariants. For example, if K ⊂ Σ× I is \mathbb Z/2 null-homologous and slice, we show that its signatures vanish and its determinants are perfect squares. These statements are derived from a cobordism result for closed unoriented surfaces in certain 4-manifolds. The Brown invariants are defined for \mathbb Z/2 null-homologous links in thickened surfaces. They take values in \mathbb Z/8 ∪ \∞\ and depend on a choice of spanning surface. We present two equivalent methods to defining and computing them, and we prove a chromatic duality result relating the two. We study their concordance properties, and we show how to interpret them as Arf invariants for null-homologous links. The Brown invariants and knot signatures are shown to be invariant under concordance of spanning surfaces.