The Branch Locus for One-Dimensional Pisot Tiling Spaces

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dc.creatorBarge, Marcy
dc.creatorDiamond, Beverly
dc.creatorSwanson, Richard
dc.date2008-04-06
dc.date.accessioned2026-07-07T09:30:45Z
dc.date.available2026-07-07T09:30:45Z
dc.descriptionIf 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.
dc.description22 pages 1 figure
dc.identifierhttps://arxiv.org/abs/0804.0930
dc.identifierhttp://arxiv.org/abs/0804.0930
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158218
dc.subjectDynamical Systems
dc.subjectAlgebraic Topology
dc.subject37B05;37A30;37B50;54H20
dc.titleThe Branch Locus for One-Dimensional Pisot Tiling Spaces
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