Graev ultrametrics and free products of Polish groups
Konstantin Slutsky
TL;DR
This paper develops Graev ultrametrics for free products and HNN extensions of Polish groups, and introduces a notion of free product for general Polish groups, demonstrating embeddings into a universal Polish group.
Contribution
It introduces a new construction of Graev ultrametrics on free products and HNN extensions, and defines a free product concept for Polish groups with embedding results.
Findings
Constructed Graev ultrametrics on free products and HNN extensions.
Proved embeddings of Polish groups into a universal Polish group.
Established a notion of free product for general Polish groups.
Abstract
We construct Graev ultrametrics on free products of groups with two-sided invariant ultrametrics and HNN extensions of such groups. We also introduce a notion of a free product of general Polish groups and prove, in particular, that two Polish groups G and H can be embedded into a Polish group T in such a way that the subgroup of T generated by G and H is isomorphic to the free product G*H.
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