Topological Invariants for Projection Method Patterns

Released on by Alan Forrest
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  • Topological Invariants for Projection Method Patterns Book Detail

  • Author : Alan Forrest
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 137
  • ISBN 13 : 0821829653
  • File Size : 1,1 MB
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Topological Invariants for Projection Method Patterns by Alan Forrest PDF Summary

Book Description: This memoir develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns, particularly the quasiperiodic patterns, constructed by the projection of a strip of a high dimensional integer lattice to a smaller dimensional Euclidean space. In the first half of the memoir the acceptance domain is very general - any compact set which is the closure of its interior - while in the second half the authors concentrate on the so-called canonical patterns. The topological invariants used are various forms of $K$-theory and cohomology applied to a variety of both $C DEGREES*$-algebras and dynamical systems derived from such a p

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Mathematics of Aperiodic Order

Mathematics of Aperiodic Order

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