THE ISOMORPHISM-PROBLEM FOR HYPERBOLIC GROUPS .1.
成果类型：
Article
署名作者：
SELA, Z
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.2307/2118520
发表日期：
1995
页码：
217-283
关键词：
摘要：
Using canonical representatives in hyperbolic groups and the decidability of the Diophantine theory of free semigroups with paired alphabet, we solve the isomorphism problem for hyperbolic groups with no (essential) small action on a real tree. The solution enables computation of the outer automorphism group of such groups and implies the homeomorphism problem for ''weakly geometric'' 3-manifolds, closed hyperbolic manifolds, and negatively curved ones of dimension greater than or equal to 5. In a continuation paper [Se1], we combine structural results on hyperbolic groups and their automorphisms obtained in [Se2] with the procedure described in this paper to give a complete solution to the isomorphism problem for (torsion-free) hyperbolic groups.