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Pattern-equivariant cohomology with integer coefficients

Published online by Cambridge University Press:  01 December 2007

LORENZO SADUN
LORENZO SADUN*
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712, USA (email: sadun@math.utexas.edu)
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Abstract

We relate Kellendonk and Putnam’s pattern-equivariant (PE) cohomology to the inverse-limit structure of a tiling space. This gives a version of PE cohomology with integer coefficients, or with values in any Abelian group. It also provides an easy proof of Kellendonk and Putnam’s original theorem relating PE cohomology to the Čech cohomology of the tiling space. The inverse-limit structure also allows for the construction of a new non-Abelian invariant, the PE representation variety.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1991 - 1998
Copyright
Copyright © Cambridge University Press 2007

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