Polynomial maps over $p$-adics and residual properties of mapping tori of group endomorphisms

TL;DR

This paper investigates the residual properties of mapping tori of free group endomorphisms, demonstrating they are virtually residually finite p-groups for almost all primes using polynomial maps over finite fields and p-adic methods.

Contribution

It establishes that these groups are virtually residually finite p-groups for all but finitely many primes, advancing understanding of their residual properties.

Findings

Groups are virtually residually finite p-groups for most primes

Uses polynomial maps over finite fields and p-adic completions

Extends previous residual property results for mapping tori

Abstract

We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method involves further studies of polynomial maps over finite fields and $p$-adic completions of number fields.