Building Groups From Restricted Diagrams of Groups

Nic Brody; Michael R. Klug

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arXiv · 2109.01939

Building Groups From Restricted Diagrams of Groups

Nic Brody·Michael R. Klug

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Abstract

We consider the problem of realizing a group as the fundamental group of a graph of groups where the vertex groups are restricted to certain classes (for example, coming from a certain finite list of groups, or having bounded geometric rank). We show how this places restrictions on the possible groups that can be realized and we give a topological application of our results to the problem of constructing manifolds from a finite set of "building blocks".

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Nic Brody, Michael R. Klug. 2021-09-14. Building Groups From Restricted Diagrams of Groups. https://arxiv.org/abs/2109.01939

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