Wagoner's Complexes Revisited

TL;DR

This paper extends Wagoner's representation of automorphism groups of subshifts of finite type to a broader class of groupoids, simplifying proofs and enabling new applications to automorphism groups over arbitrary groups and G-SFTs.

Contribution

It generalizes Wagoner's construction to groupoids with a refinement structure, streamlining proofs and broadening applicability to various automorphism groups.

Findings

Streamlined proof of Wagoner's representation

Extended automorphism group construction to arbitrary finitely generated groups

Applied to automorphism groups of G-SFTs

Abstract

We generalize Wagoner's representation of the automorphism group of a two-sided subshifts of finite type as the fundamental group of a certain CW-complex to groupoids having a certain refinement structure. This significantly streamlines the original proof and allows us to extend this construction to, e.g., the automorphism group of subshifts of finite type over arbitrary finitely generated groups and the automorphism group of G-SFTs.