On the isolated points in the space of groups

By Yves Cornulier, Luc Guyot, W. Pitsch. 2005

66 citations recorded by the source corpus.

We investigate the isolated points in the space of finitely generated groups. We give a workable characterization of isolated groups and study their hereditary properties. Various examples of groups are shown to yield isolated groups. We also discuss a connection between isolated groups and solvability of the word problem.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0f491040d5fd7b8e937a3026968091980ac74233

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In Computational Theory and Mathematics

1. Martin R. Bridson
2. V. Kleptsyn
3. Pierre de la Harpe

In Discrete Mathematics and Combinatorics

1. Martin R. Bridson
2. Pierre de la Harpe

In Geometry and Topology

1. Martin R. Bridson
2. V. Kleptsyn
3. Pierre de la Harpe

Citations in the corpus

• The Chabauty space of closed subgroups of the three-dimensional Heisenberg group (2007, background): “In particular, if Fk is the free group on k generators, N(Fk) is the space of marked groups on k generators, which has been the subject of much work since its appearance in the final remarks of [Gromov 1981]; see among others [Grigorchuk 1984; Champetier 2000; Champetier and Guirardel 2005; de Cornu”