Within group theory, geometric group theory studies groups by equipping them with a metric and thus regarding them as metric spaces.
For finitely generated groups this is typically done by regarding the group’s elements as the vertices of a graph – the Cayley graph – whose edges connect elements related by multiplication with a generator. The corresponding graph distance then equips the group with a metric.
The methods of geometric group theory overlap with kernel methods in machine learning.
Textbooks accounts:
Persi Diaconis, Chapter 6 of: Group Representations in Probability and Statistics, Lecture Notes - Monographs Series, Institute of Mathematical Statistics 1988 (pdf)
Cornelia Druţu, Michael Kapovich (appendix by Bogdan Nica), Geometric group theory, Colloquium Publications 63, AMS 2018 (ISBN:978-1-4704-1104-6, pdf)
Clara Löh, Geometric Group Theory, Springer 2017 (doi:10.1007/978-3-319-72254-2, pdf)
See also:
Last revised on May 9, 2021 at 10:22:14. See the history of this page for a list of all contributions to it.