奥特空间简单闭包的度定理

IF 0.8 4区数学 Q2 MATHEMATICS Homology Homotopy and Applications 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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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.

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