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July  2009, 23(3): 847-865. doi: 10.3934/dcds.2009.23.847

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, United States
2. 

Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, United States

Received  October 2007 Revised  June 2008 Published  November 2008

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.
Citation: Natalie Priebe Frank, Lorenzo Sadun. Topology of some tiling spaces without finite local complexity. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 847-865. doi: 10.3934/dcds.2009.23.847
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