Deep pockets in lattices and other groups

Abstract

We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol'skii. We then give examples of important groups (such as Nil and Sol) which have deep pockets.

19 pages; added Section 3 on Euclidean groups

Cited by in corpus (2)

• A group with deep pockets for all finite generating sets
• The language of geodesics for the discrete Heisenberg group