2023/04/05 by David Cimasoni, Cimasoni, David, Maciej Markiewicz +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #55N25 (Secondary) #57K10 (Primary) 57M05 #Advanced Combinatorial Mathematics #Biological Activity of Diterpenoids and Biflavonoids #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2304.02347
openalex publication_date 2023/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the limits of the multivariable signature function σL of a μ-component link L as some variable tends to 1 via two different approaches: a three-dimensional and a four-dimensional one. The first uses the definition of σL by generalized Seifert surfaces and forms. The second relies on a new extension of σL from its usual domain (S1∖\1\)μ to the full torus \mathbbTμ together with a Torres-type formula for σL, results which are of independent interest. Among several consequences, we obtain new estimates on the value of the Levine-Tristram signature of a link close to 1.