对合的布尔复形

Pub Date : 2022-12-28 DOI:10.1007/s00026-022-00629-9

Axel Hultman, Vincent Umutabazi

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引用次数: 0

摘要

设（W，S）是一个Coxeter系统。我们引入了W的对合布尔复形，它是Ragnarsson和Tenner研究的W的布尔复形的一个类似物。通过应用离散Morse理论，我们确定了一大类（W，S）（包括所有有限Coxeter群）对合布尔复形的同伦型，发现该同伦型是一个维数为\（\vert S\vert-1\）的球楔的同伦类型。此外，我们还找到了楔中球体数量的简单递推公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Boolean Complexes of Involutions

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Boolean Complexes of Involutions

Let (W, S) be a Coxeter system. We introduce the boolean complex of involutions of W which is an analogue of the boolean complex of W studied by Ragnarsson and Tenner. By applying discrete Morse theory, we determine the homotopy type of the boolean complex of involutions for a large class of (W, S), including all finite Coxeter groups, finding that the homotopy type is that of a wedge of spheres of dimension \(\vert S\vert -1\). In addition, we find simple recurrence formulas for the number of spheres in the wedge.

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