The branch locus for one-dimensional Pisot tiling spaces

Marcy Barge, Beverly Diamond, and Richard Swanson. "The branch locus for one-dimensional Pisot tiling spaces." Fundamenta Mathematicae 204.3 (2009): 215-240. <http://eudml.org/doc/282875>.

@article{MarcyBarge2009,
abstract = {If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space $_\{Φ\}$ factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.},
author = {Marcy Barge, Beverly Diamond, Richard Swanson},
journal = {Fundamenta Mathematicae},
keywords = {tiling space; Pisot substitution; geometric realization; branch locus},
language = {eng},
number = {3},
pages = {215-240},
title = {The branch locus for one-dimensional Pisot tiling spaces},
url = {http://eudml.org/doc/282875},
volume = {204},
year = {2009},
}

TY - JOUR
AU - Marcy Barge
AU - Beverly Diamond
AU - Richard Swanson
TI - The branch locus for one-dimensional Pisot tiling spaces
JO - Fundamenta Mathematicae
PY - 2009
VL - 204
IS - 3
SP - 215
EP - 240
AB - If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space $_{Φ}$ factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.
LA - eng
KW - tiling space; Pisot substitution; geometric realization; branch locus
UR - http://eudml.org/doc/282875
ER -