Examples of amalgamated free products and coupling rigidity
Yoshikata Kida
TL;DR
This paper explores amalgamated free products that exhibit coupling rigidity related to their Bass-Serre trees, leading to new orbit equivalence rigidity results for certain mapping class group products.
Contribution
It introduces amalgamated free products with coupling rigidity and applies this to establish orbit equivalence rigidity for products of mapping class groups.
Findings
Amalgamated free products satisfying coupling rigidity.
Orbit equivalence rigidity for mapping class group products.
Abstract
We present amalgamated free products satisfying coupling rigidity with respect to the automorphism group of the associated Bass-Serre tree. As an application, we obtain orbit equivalence rigidity for amalgamated free products of mapping class groups.
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