On the distribution of Alexander polynomials in certain families of closed braids

TL;DR

This paper investigates how Alexander polynomials' arithmetic invariants distribute across specific families of links derived from braids, drawing parallels with number theory and class group distributions to advance arithmetic topology.

Contribution

It introduces a new perspective on the distribution of Alexander polynomial invariants in braid-derived link families, connecting topology with number theory.

Findings

Distribution patterns of Alexander polynomial invariants analyzed

Analogies with class group distributions established

New directions proposed in arithmetic topology

Abstract

We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links we consider arise from braids on a fixed number of strings. We explore analogies with number theory and the distribution of class groups in various families of number fields, setting out new directions in arithmetic topology and arithmetic statistics.