2009/06/23 by Housem Boulmezaoud, Boulmezaoud, Housem, Johannes Kellendonk +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #math.DS
paper · pdf · doi:10.48550/arxiv.0906.4308
openalex publication_date 2009/06/23 · arxiv created 2010/05/31 · arxiv updated 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-Gähler complex, the second is the recently introduced PV-cohomolgy of Bellissard and Savinien 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.