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

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