On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups

被引：3

作者：

Bridson, Martin R. ^{[2
]}

Reeves, Lawrence ^{[1
]}

机构：

[1] Univ Melbourne, Dept Math & Stat, Parkville, Vic 3010, Australia

[2] Univ Oxford, Math Inst, Oxford OX1 3LB, England

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 08期

基金：

英国工程与自然科学研究理事会;

关键词：

geometric group theory; automatic groups; isomorphism problem;

D O I：

10.1007/s11425-011-4212-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the isomorphism problem is solvable in the class of central extensions of word-hyperbolic groups, and that the isomorphism problem for biautomatic groups reduces to that for biautomatic groups with finite centre. We describe an algorithm that, given an arbitrary finite presentation of an automatic group I", will construct explicit finite models for the skeleta of K(I", 1) and hence compute the integral homology and cohomology of I".

引用

页码：1533 / 1545

页数：13

共 18 条

[1] On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
Martin R. Bridson
Lawrence Reeves
Science China Mathematics, 2011, 54
[2] On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
BRIDSON Martin R.
REEVES Lawrence
Science China(Mathematics), 2011, 54 (08) : 1533 - 1545
[3] On the isomorphism problem for even Artin groups
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Paris, Luis
JOURNAL OF ALGEBRA, 2022, 607 : 35 - 52
[4] The Isomorphism Problem for All Hyperbolic Groups
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Vincent Guirardel
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[5] The Isomorphism Problem for All Hyperbolic Groups
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Guirardel, Vincent
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2011, 21 (02) : 223 - 300
[6] On the isomorphism problem for even Artin groups
Blasco-Garcia, Ruben
Paris, Luis
JOURNAL OF ALGEBRA, 2022, 607 : 35 - 52
[7] The isomorphism problem for toral relatively hyperbolic groups
François Dahmani
Daniel Groves
Publications mathématiques, 2008, 107 : 211 - 290
[8] On rigidity and the isomorphism problem for tree braid groups
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GROUPS GEOMETRY AND DYNAMICS, 2009, 3 (03) : 469 - 523
[9] The Baumslag-Solitar Groups: A Solution for the Isomorphism Problem
Clement, Anthony E.
ASPECTS OF INFINITE GROUPS, 2008, 1 : 75 - 79
[10] On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces
Hartz, Michael
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2017, 69 (01): : 54 - 106

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