Trees, homology, and automorphism groups of right-angled Artin groups

被引：0

作者：

Aramayona, Javier ^{[1
,2
]}

Fernandez, Jose L. ^{[1
]}

Fernandez, Pablo ^{[1
]}

Martinez-Perez, Conchita ^{[3
]}

机构：

[1] Univ Autonoma Madrid, Dept Math, E-28049 Madrid, Spain

[2] ICMAT, Madrid 28049, Spain

[3] Univ Zaragoza, Dept Math, Pedro Cerbuna S-N, E-50009 Zaragoza, Spain

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2019年 / 50卷 / 03期

关键词：

Automorphism groups; RAAGs; Trees; Betti numbers; Lower bounds; Symbolic method; Exponential generating functions;

D O I：

10.1007/s10801-018-0854-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree.

引用

页码：293 / 315

页数：23

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