Completely Metrisable Groups Acting on Trees

2010/09/30 by Christian Rosendal, Rosendal, Christian
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #math.GR #math.LO

paper · pdf · doi:10.48550/arxiv.1009.6208

arxiv created 2010/09/30 · arxiv updated 2010/10/01

Abstract

We consider actions of completely metrisable groups on simplicial trees in the context of the Bass--Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any decomposition as a free product with amalgamation, G=A∗_CB, the amalgamated groups A, B and C are open in G.

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