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Exotic Actions on Trees
Author(s) -
Holton Charles,
Zamboni Luca Q.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002652
Subject(s) - mathematics , action (physics) , tree (set theory) , interval (graph theory) , combinatorics , unit interval , automorphism , unit (ring theory) , automorphism group , translation (biology) , discrete mathematics , pure mathematics , mathematics education , biochemistry , chemistry , physics , quantum mechanics , messenger rna , gene
We give an explicit example of an exotic (non‐simplicial), geometric free action of the free group F 3 on an R‐tree T . We begin by associating an interval translation mapping of the unit interval to an automorphism ψ of F 3 . We use a result of D. Gaboriau and G. Levitt to obtain an F 3 ‐action on an R‐tree T . We show that for our particular choice of ψ, the resulting F 3 ‐action is minimal, free and exotic. 1991 Mathematics Subject Classification 20E36.
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