Number of orbits of branch points of $\textbf {R}$-trees
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- by Renfang Jiang PDF
- Trans. Amer. Math. Soc. 335 (1993), 341-368 Request permission
Abstract:
An $R$-tree is a metric space in which any two points are joined by a unique arc. Every arc is isometric to a closed interval of $R$ . When a group $G$ acts on a tree ($Z$-tree) $X$ without inversion, then $X/G$ is a graph. One gets a presentation of $G$ from the quotient graph $X/G$ with vertex and edge stabilizers attached. For a general $R$-tree $X$, there is no such combinatorial structure on $X/G$. But we can still ask what the maximum number of orbits of branch points of free actions on $R$-trees is. We prove the finiteness of the maximum number for a family of groups, which contains free products of free abelian groups and surface groups, and this family is closed under taking free products with amalgamation.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 335 (1993), 341-368
- MSC: Primary 20E08; Secondary 20E06, 20F32, 57M07
- DOI: https://doi.org/10.1090/S0002-9947-1993-1107026-4
- MathSciNet review: 1107026