arxiv:2510.01516

Immersions of complexes of groups

Published on Oct 1

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Abstract

A new class of complexes of groups is constructed to record local data, and a notion of immersion is introduced, proving that locally isometric immersions into non-positively curved complexes are π₁-injective and induce isometric embeddings.

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Given a complex of groups, we construct a new class of complex of groups that records its local data and offer a functorial perspective on the statement that complexes of groups are locally developable. We also construct a new notion of an immersion of complexes of groups and establish that a locally isometric immersion of a complex of groups into a non-positively curved complex of groups is pi_1-injective. Furthermore, the domain complex of groups is developable and the induced map on geometric realizations of developments is an isometric embedding.

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