Geodesic
The branch locus for one-dimensional Pisot tiling spaces
Marcy Barge 1   ; Beverly Diamond 2   ; Richard Swanson 1
1 Department of Mathematics Montana State University Bozeman, MT 59717, U.S.A.
2 Department of Mathematics College of Charleston Charleston, SC 29424, U.S.A.
Fundamenta Mathematicae, Tome 204 (2009) no. 3, pp. 215-240 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/fm204-3-2
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

Marcy Barge  1   ; Beverly Diamond  2   ; Richard Swanson  1

1 Department of Mathematics Montana State University Bozeman, MT 59717, U.S.A.
2 Department of Mathematics College of Charleston Charleston, SC 29424, U.S.A. 
@article{10_4064_fm204_3_2,
     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},
     year = {2009},
     volume = {204},
     number = {3},
     doi = {10.4064/fm204-3-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm204-3-2/}
}
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
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
%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

Cité par Sources :