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Fibre products, non-positive curvature, and decision problems |
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| Authors: | G. Baumslag M. R. Bridson C. F. Miller III H. Short |
| Affiliation: | (1) Department of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, NY 10031, USA, e-mail: gilbert@groups.sci.ccny.cuny.edu, US;(2) Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, U.K., e-mail: bridson@maths.ox.ac.uk, UK;(3) Department of Mathematics and Statistics, University of Melbourne, Parkville 3052, Australia, e-mail: cfm@ms.unimelb.edu.au, AU;(4) Centre de Mathématiques et d'Informatique, Rue Joliot--Curie, Université de Provence, F--13453 Marseille cedex 13, France, e-mail: hamish@claudia.univ-mrs.fr, FR |
| Abstract: | We give a criterion for fibre products to be finitely presented and use it as the basis of a construction that encodes the pathologies of finite group presentations into pairs of groups where G is a product of hyperbolic groups and P is a finitely presented subgroup. This enables us to prove that there is a finitely presented subgroup P in a biautomatic group G such that the generalized word problem for is unsolvable and P has an unsolvable conjugacy problem. An additional construction shows that there exists a compact non-positively curved polyhedron X such that is biautomatic and there is no algorithm to decide isomorphism among the finitely presented subgroups of . Received: October 7, 1999. |
| Keywords: | . Finitely presented groups fibre products decision problems non-positive curvature hyperbolic groups automatic groups. |
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