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- W769969584 abstract "For every free product decomposition $G = G_{1} ast ...ast G_{q} ast F_{r}$ of a group of finite Kurosh rank $G$, where $F_r$ is a finitely generated free group, we can associate some (relative) outer space $mathcal{O}$. We study the asymmetry of the Lipschitz metric $d_R$ on the (relative) Outer space $mathcal{O}$. More specifically, we generalise the construction of Algom-Kfir and Bestvina, introducing an (asymmetric) Finsler norm $|cdot|^{L}$ that induces $d_R$. Let's denote by $Out(G, mathcal{O})$ the outer automorphisms of $G$ that preserve the set of conjugacy classes of $G_i$'s. Then there is an $Out(G, mathcal{O})$-invariant function $Psi : mathcal{O} rightarrow mathbb{R}$ such that when $| cdot |^{L}$ is corrected by $d Psi$, the resulting norm is quasisymmetric. As an application, we prove that if we restrict $d_R$ to the $epsilon$-thick part of the relative Outer space for some $epsilon >0$, is quasi-symmetric . Finally, we generalise for IWIP automorphisms of a free product a theorem of Handel and Mosher, which states that there is a uniform bound which depends only on the group, on the ratio of the relative expansion factors of any IWIP $phi in Out(F_n)$ and its inverse." @default.
- W769969584 created "2016-06-24" @default.
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- W769969584 date "2015-07-07" @default.
- W769969584 modified "2023-09-27" @default.
- W769969584 title "Asymmetry of Outer Space of a free product" @default.
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