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The branch locus for one-dimensional Pisot tiling spaces

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Barge M., Diamond B., Swanson R.

Fundamenta Mathematicae

2009

tom 204

nr 3

215-240

If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space $𝓣_{Φ}$ 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Barge M.

1 Diamond B.

1 Swanson R.

1 2009

Wyniki wyszukiwania

The branch locus for one-dimensional Pisot tiling spaces