nLab
geometric group theory

Contents

Contents

Idea

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.

References

Textbooks accounts:

See also:

Last revised on May 9, 2021 at 06:22:14. See the history of this page for a list of all contributions to it.