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ℝ‐trees and laminations for free groups II: the dual lamination of an ℝ‐tree
Author(s) -
Coulbois Thierry,
Hilion Arnaud,
Lustig Martin
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn053
Subject(s) - lamination , tree (set theory) , boundary (topology) , focus (optics) , mathematics , dual (grammatical number) , space (punctuation) , equivariant map , pure mathematics , geometry , combinatorics , computer science , mathematical analysis , physics , materials science , composite material , optics , art , layer (electronics) , operating system , literature
We define a dual lamination for any isometric very small F N ‐action on an ℝ‐tree T . We obtain an Out ( F N )‐equivariant map from the boundary of the outer space to the space of laminations. This map generalizes the corresponding basic construction for surfaces. It fails to be continuous. We then focus on the case where the tree T has dense orbits. In this case, we give two other equivalent constructions, but of different nature, of the dual lamination.