Deck transformations of developable complexes of groups

TL;DR

This paper introduces deck transformations for developable complexes of groups, proposing a new universal development construction based on path equivalence classes, and characterizes the group of deck transformations.

Contribution

It presents a novel framework for deck transformations in developable complexes of groups and offers an alternative universal development construction inspired by classical covering theory.

Findings

Provides a natural characterization of the group of deck transformations.

Introduces an alternative construction of the universal development.

Draws parallels with classical covering theory for topological spaces.

Abstract

We introduce the concept of deck transformations within the category of developable complexes of groups. Drawing inspiration from classical covering theory for topological spaces, we propose an alternative construction of the universal development of a developable complex of groups, formulated in terms of equivalence classes of paths. This framework allows us to provide a natural characterization of the group of deck transformations.