Graev metrics on free products and HNN extensions
Konstantin Slutsky
TL;DR
This paper develops a method to construct two-sided invariant metrics on free products and HNN extensions of groups with such metrics, extending Graev's approach for free groups over pointed metric spaces.
Contribution
It introduces a new construction of invariant metrics on free products and HNN extensions, generalizing Graev's metric construction to broader group structures.
Findings
Constructed two-sided invariant metrics on free products with amalgamation.
Extended Graev's metric construction to HNN extensions.
Provided conditions under which these metrics exist.
Abstract
We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the Graev's construction of metrics on free groups over pointed metric spaces
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology