On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
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 a...
| Autori principali: | , |
|---|---|
| Natura: | Journal article |
| Lingua: | English |
| Pubblicazione: |
2011
|
| _version_ | 1826264446809407488 |
|---|---|
| author | Bridson, M Reeves, L |
| author_facet | Bridson, M Reeves, L |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | 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 Γ, will construct explicit finite models for the skeleta of K(Γ, 1) and hence compute the integral homology and cohomology of Γ. © 2011 Science China Press and Springer-Verlag Berlin Heidelberg. |
| first_indexed | 2024-03-06T20:07:56Z |
| format | Journal article |
| id | oxford-uuid:298b062f-db34-4cf7-a31f-4766750d0cab |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:07:56Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:298b062f-db34-4cf7-a31f-4766750d0cab2022-03-26T12:19:47ZOn the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:298b062f-db34-4cf7-a31f-4766750d0cabEnglishSymplectic Elements at Oxford2011Bridson, MReeves, LWe 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 Γ, will construct explicit finite models for the skeleta of K(Γ, 1) and hence compute the integral homology and cohomology of Γ. © 2011 Science China Press and Springer-Verlag Berlin Heidelberg. |
| spellingShingle | Bridson, M Reeves, L On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| title | On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| title_full | On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| title_fullStr | On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| title_full_unstemmed | On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| title_short | On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| title_sort | on the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups |
| work_keys_str_mv | AT bridsonm onthealgorithmicconstructionofclassifyingspacesandtheisomorphismproblemforbiautomaticgroups AT reevesl onthealgorithmicconstructionofclassifyingspacesandtheisomorphismproblemforbiautomaticgroups |