奥特空间简单闭包的度定理

Pub Date : 2024-05-01 DOI:10.4310/hha.2024.v26.n1.a13

Juliet Aygun, Jeremy Miller

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引用次数: 0

摘要

基于图的度数是一般扰动后基本非基点顶点的数目。Hatcher-Vogtmann 的阶数定理指出，阶数最多为 $d$ 的图的 Auter 空间子复数是 $(d-1)$ 连接的。我们将度的定义扩展到 Auter 空间的简单闭包，并在此背景下证明了 Hatcher-Vogtmann 结果的一个版本。

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A degree theorem for the simplicial closure of Auter Space

The degree of a based graph is the number of essential non-basepoint 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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