2010-09-01, English, Article, Journal or magazine article edition: Comparing different versions of tiling cohomology. Boulmezaoud, Housem; Kellendonk, Johannes

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Physical Description
  • Magazine/​Journal article
Published
  • Elsevier B.V., 2010 Sept 1
Language
  • English

Edition details

Title
  • Comparing different versions of tiling cohomology.
Appears In
  • Topology and its Applications, v.157, no.14, 2010 Sept 1, p.2225(15) (ISSN: 0166-8641)
Author
  • Boulmezaoud, Housem
  • Kellendonk, Johannes
Published
  • Elsevier B.V., 2010 Sept 1
Physical Description
  • Magazine/​Journal article
Subjects
Target Audience
  • Academic
Summary
  • To link to full-text access for this article, visit this link: http:/​/​dx.doi.org/​10.1016/​j.topol.2010.06.004 Byline: Housem Boulmezaoud, Johannes Kellendonk Keywords: Aperiodic tilings; Cohomology; Pattern equivariant; de Rham theorem Abstract: We establish direct isomorphisms between different versions of tiling cohomology. The first version is the direct limit of the cohomologies of the approximants in the Anderson-Putnam-Gahler system, the second is the recently introduced PV-cohomology of Savinien and Bellissard and the third is pattern equivariant cohomology. For the last two versions one can define weak cohomology groups. We show that the isomorphisms extend to the weak versions. This leads to an alternative formulation of the pattern equivariant mixed quotient group which describes deformations of the tiling modulo topological conjugacy. Author Affiliation: Universite de Lyon, Universite Claude Bernard Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne cedex, France Article History: Received 2 November 2009; Revised 1 June 2010; Accepted 2 June 2010
Terms of Use
  • COPYRIGHT 2010 Elsevier B.V.
Language
  • English
Database
  • Gale Academic OneFile
Identifier
  • 232000735

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