Deformation spaces of trees | Zendy

Vincent Guirardel | Zendy; Gilbert Levitt | Zendy

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Deformation spaces of trees

Author(s) -

Vincent Guirardel,

Gilbert Levitt

Publication year - 2007

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/8

Subject(s) - contractible space , mathematics , deformation (meteorology) , tree (set theory) , space (punctuation) , point (geometry) , pure mathematics , topology (electrical circuits) , combinatorics , geometry , computer science , physics , meteorology , operating system

Let G be a finitely generated group. Two simplicial G-trees are said to be inthe same deformation space if they have the same elliptic subgroups (if H fixesa point in one tree, it also does in the other). Examples includeCuller-Vogtmann's outer space, and spaces of JSJ decompositions. We discusswhat features are common to trees in a given deformation space, how to passfrom one tree to all other trees in its deformation space, and the topology ofdeformation spaces. In particular, we prove that all deformation spaces arecontractible complexes.

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