Topology of some tiling spaces without finite local complexity

Natalie Priebe Frank; Lorenzo Sadun

doi:10.3934/dcds.2009.23.847

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2009, Volume 23, Issue 3: 847-865. Doi: 10.3934/dcds.2009.23.847

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Topology of some tiling spaces without finite local complexity

Natalie Priebe Frank^1, and
Lorenzo Sadun^2,

1.
Department of Mathematics, Vassar College, Poughkeepsie, NY 12604
2.
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712

Received: September 30, 2007

Revised: May 31, 2008

Published: August 2009

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Abstract

A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have "fault lines", along which tiles can slide past one another. We investigate the topology of a certain class of tiling spaces of this type. We show that they can be written as inverse limits of CW complexes, and their Čech cohomology is related to properties of the fault lines.

Keywords:

Self-similar tilings,
tiling dynamical systems.

Mathematics Subject Classification: Primary: 37B50, Secondary: 52C23, 54F65, 37C85.

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