The average signature of graph links
Maciej Borodzik, Jadwiga Sosnowska
TL;DR
This paper generalizes the computation of the average Tristram-Levine signature for graph links with positive weights in a three-sphere, using advanced algebraic tools and reciprocity laws.
Contribution
It introduces a method to compute equivariant signatures of graph links with positive weights, extending previous results by Kirby and Melvin.
Findings
Derived a formula for the average signature of graph links
Applied Neumann's algorithm and Dedekind sum reciprocity law
Extended signature computations to weighted graph links
Abstract
We compute the average Tristram---Levine signature of any graph link with positive weights in a three sphere, generalizing the results of Kirby and Melvin. The main tools are the Neumann's algorithm for computing the equivariant signatures of graph links and the Reciprocity Law for Dedekind sums.
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