The Branch Locus for One-Dimensional Pisot Tiling Spaces
Dynamical Systems
2008-04-08 v1 Algebraic Topology
Abstract
If phi is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Phi on the tiling space T_Phi factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Phi-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.
Cite
@article{arxiv.0804.0930,
title = {The Branch Locus for One-Dimensional Pisot Tiling Spaces},
author = {Marcy Barge and Beverly Diamond and Richard Swanson},
journal= {arXiv preprint arXiv:0804.0930},
year = {2008}
}
Comments
22 pages 1 figure