Geodesic
The branch locus for one-dimensional Pisot tiling spaces
Marcy Barge1 ; Beverly Diamond2 ; Richard Swanson1
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.

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.
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. 
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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. http://geodesic.mathdoc.fr/articles/10.4064/fm204-3-2/

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