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- Title
Geometries of topological groups.
- Authors
Rosendal, Christian
- Abstract
The paper provides an overarching framework for the study of some of the intrinsic geometries that a topological group may carry. An initial analysis is based on geometric nonlinear functional analysis, that is, the study of Banach spaces as metric spaces up to various notions of isomorphism, such as bi-Lipschitz equivalence, uniform homeomorphism, and coarse equivalence. This motivates the introduction of the various geometric categories applicable to all topological groups, namely, their uniform and coarse structure, along with those applicable to a more select class, that is, (local) Lipschitz and quasimetric structure. Our study touches on Lie theory, geometric group theory, and geometric nonlinear functional analysis and makes evident that these can all be seen as instances of a single coherent theory.
- Subjects
TOPOLOGICAL groups; NONLINEAR functional analysis; METRIC spaces; BANACH spaces; UNIFORM spaces; FUNCTIONAL analysis
- Publication
Bulletin (New Series) of the American Mathematical Society, 2023, Vol 60, Issue 4, p539
- ISSN
0273-0979
- Publication type
Article
- DOI
10.1090/bull/1807