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This research constructs a new class of complex of groups and identifies locally isometric immersions, suggesting their importance in group theory.
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 π₁-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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Jagerynn Ting Verano (2025) studied this question.
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