2014
KTheory of Crossed Products of Tiling C*Algebras by Rotation Groups
Publication
Publication
Communications in Mathematical Physics , Volume 334  Issue 1 p. 301 311
Let Ω be a tiling space and let G be the maximal group of rotations which fixes Ω. Then the cohomology of Ω and Ω/G are both invariants which give useful geometric information about the tilings in Ω. The noncommutative analog of the cohomology of Ω is the Ktheory of a C*algebra associated to Ω, and for translationally finite tilings of dimension 2 or less, the Ktheory is isomorphic to the direct sum of cohomology groups. In this paper we give a prescription for calculating the noncommutative analog of the cohomology of Ω/G, that is, the Ktheory of the crossed product of the tiling C*algebra by G. We also provide a table with some calculated Kgroups for many common examples, including the Penrose and pinwheel tilings.
Additional Metadata  

dx.doi.org/10.1007/s0022001420705  
Communications in Mathematical Physics  
Starling, C. (2014). KTheory of Crossed Products of Tiling C*Algebras by Rotation Groups. Communications in Mathematical Physics, 334(1), 301–311. doi:10.1007/s0022001420705
