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- W2749748165 abstract "Let $G$ be a finitely generated group. Given two length functions $ell$ and $m$ of irreducible $G$ actions on real trees $A$ and $B$, when is the point-wise sum $ell + m$ again the length function of an irreducible $G$ action on a real tree? In this article we show that additivity is equivalent to the existence of a common refinement of $A$ and $B$, this equivalence is established using Guirardel's core. Moreover, in this case the sum $ell + m$ is the length function of the common refinement of $A$ and $B$ given explicitly by the Guirardel core. We also give a combinatorial characterization of compatibility, generalizing a criterion given by Behrstock, Bestvina, and Clay for free group actions on simplicial trees. This compatibility condition characterizes the convex geometry, in the vector space of class functions, of common deformation spaces of irreduicble actions on real trees, such as the closure of Culler-Vogtmann Outer Space or the space of small actions of a hyperbolic group $G$." @default.
- W2749748165 created "2017-08-31" @default.
- W2749748165 creator A5015603309 @default.
- W2749748165 date "2017-08-23" @default.
- W2749748165 modified "2023-09-27" @default.
- W2749748165 title "Length Function Compatibility for Group Actions on Real Trees" @default.
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