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arXiv · 2208.12358

A degree theorem for the simplicial closure of Auter space

Juliet Aygun·Jeremy Miller
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Abstract

The degree of a based graph is the number of essential nonbasepoint vertices after generic perturbation. Hatcher--Vogtmann's degree theorem states that the subcomplex of Auter space of graphs of degree at most d is (d-1)-connected. We extend the definition of degree to the simplicial closure of Auter space and prove a version of Hatcher--Vogtmann's result in this context.

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Juliet Aygun, Jeremy Miller. 2022-08-25. A degree theorem for the simplicial closure of Auter space. https://arxiv.org/abs/2208.12358

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