Embedding tiling spaces in surfaces

Charles Holton, and Brian F. Martensen. "Embedding tiling spaces in surfaces." Fundamenta Mathematicae 201.2 (2008): 99-113. <http://eudml.org/doc/283385>.

@article{CharlesHolton2008,
abstract = {We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms in terms of asymptotic composants of substitutions.},
author = {Charles Holton, Brian F. Martensen},
journal = {Fundamenta Mathematicae},
keywords = {tiling spaces; pseudo-Anosov; surface embeddings; interval exchange transformations; free group automorphisms},
language = {eng},
number = {2},
pages = {99-113},
title = {Embedding tiling spaces in surfaces},
url = {http://eudml.org/doc/283385},
volume = {201},
year = {2008},
}

TY - JOUR
AU - Charles Holton
AU - Brian F. Martensen
TI - Embedding tiling spaces in surfaces
JO - Fundamenta Mathematicae
PY - 2008
VL - 201
IS - 2
SP - 99
EP - 113
AB - We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms in terms of asymptotic composants of substitutions.
LA - eng
KW - tiling spaces; pseudo-Anosov; surface embeddings; interval exchange transformations; free group automorphisms
UR - http://eudml.org/doc/283385
ER -