Integral cohomology of rational projection method patterns
نویسندگان
چکیده
منابع مشابه
Integral Cohomology of Rational Projection Method Patterns
We study the cohomology and hence K-theory of the aperiodic tilings formed by the so called ‘cut and project’ method, i.e., patterns in d dimensional Euclidean space which arise as sections of higher dimensional, periodic structures. They form one of the key families of patterns used in quasicrystal physics, where their topological invariants carry quantum mechanical information. Our work devel...
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Aperiodic point sets (or tilings) which can be obtained by the method of cut and projection from higher dimensional periodic sets play an important role for the description of quasicrystals. Their topological invariants can be computed using the higher dimensional periodic structure. We report on the results obtained for the cohomology groups of projection point patterns supplemented by explici...
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It is not known whether or not the stable rational cohomology groups H̃∗(Aut(F∞);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions.) We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabili...
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We define the cohomology of a tiling as the cocycle cohomology of its associated groupoid and consider this cohomology for the class of tilings which are obtained from a higher dimensional lattice by the canonical projection method in Schlottmann’s formulation. We prove the cohomology to be equivalent to a certain cohomology of the lattice. We discuss one of its qualitative features, namely tha...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2013
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2013.13.1661