The branch locus for one-dimensional Pisot tiling spaces
Fundamenta Mathematicae, Tome 204 (2009) no. 3, pp. 215-240
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
If $\varphi$ is a Pisot substitution of degree $d$, then the
inflation and substitution homeomorphism $\mit\Phi$ on the tiling space ${\cal T}_{\mit\Phi}$
factors via geometric realization onto a
$d$-dimensional solenoid. Under this realization, the collection of
$\mit\Phi$-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.
Keywords:
varphi pisot substitution degree inflation substitution homeomorphism mit phi tiling space cal mit phi factors via geometric realization d dimensional solenoid under realization collection mit phi periodic asymptotic tilings corresponds finite set projects branch locus d torus prove tiling spaces homeomorphic resulting branch loci the action certain affine maps torus
Affiliations des auteurs :
Marcy Barge 1 ; Beverly Diamond 2 ; Richard Swanson 1
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author = {Marcy Barge and Beverly Diamond and Richard Swanson},
title = {The branch locus for one-dimensional {Pisot} tiling spaces},
journal = {Fundamenta Mathematicae},
pages = {215--240},
publisher = {mathdoc},
volume = {204},
number = {3},
year = {2009},
doi = {10.4064/fm204-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm204-3-2/}
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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 SP - 215 EP - 240 VL - 204 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm204-3-2/ DO - 10.4064/fm204-3-2 LA - en ID - 10_4064_fm204_3_2 ER -
%0 Journal Article %A Marcy Barge %A Beverly Diamond %A Richard Swanson %T The branch locus for one-dimensional Pisot tiling spaces %J Fundamenta Mathematicae %D 2009 %P 215-240 %V 204 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/fm204-3-2/ %R 10.4064/fm204-3-2 %G en %F 10_4064_fm204_3_2
Marcy Barge; Beverly Diamond; Richard Swanson. The branch locus for one-dimensional Pisot tiling spaces. Fundamenta Mathematicae, Tome 204 (2009) no. 3, pp. 215-240. doi: 10.4064/fm204-3-2
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