£60.95

Topological Invariants for Projection Method Patterns (Memoirs of the American Mathematical Society)

Applied Mathematics

Price data last checked 63 day(s) ago - refreshing...

View at Amazon

Price History & Forecast

Last 28 days • 28 data points (No recent data available)

Historical

Generating forecast...

Price Distribution

Price distribution over 28 days • 1 price levels

Days at Price

Price Analysis

Most common price: £61 (28 days, 100.0%)

Price range: £61 - £61

Price levels: 1 different prices over 28 days

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 we 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 $C^*$-algebras and dynamical systems derived from such a pattern.The invariants considered all aim to capture geometric properties of the original patterns, such as quasiperiodicity or self-similarity, but one of the main motivations is also to provide an accessible approach to the the $K_0$ group of the algebra of observables associated to a quasicrystal with atoms arranged on such a pattern. The main results provide complete descriptions of the (unordered) $K$-theory and cohomology of codimension 1 projection patterns, formulae for these invariants for codimension 2 and 3 canonical projection patterns, general methods for higher codimension patterns and a closed formula for the Euler characteristic of arbitrary canonical projection patterns.Computations are made for the Ammann-Kramer tiling. Also included are qualitative descriptions of these invariants for generic canonical projection patterns. Further results include an obstruction to a tiling arising as a substitution and an obstruction to a substitution pattern arising as a projection. One corollary is that, generically, projection patterns cannot be derived via substitution systems.

Product Specifications

Format: paperback
ASIN: 0821829653
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Applied Mathematics
Domain: Amazon UK
Release Date: 26 September 2002
Listed Since: 17 October 2006

Barcode

No barcode data available

Topological Invariants for Projection Method Patterns (Memoirs of the American Mathematical Society)

Price History & Forecast

Price Distribution

Price Analysis

Description

Product Specifications

Barcode

Similar Products You Might Like

Connective Real K-theory of Finite Groups: 169 (Mathematical Surveys and Monographs)

The Beilinson Complex and Canonical Rings of Irregular Surfaces (Memoirs of the American Mathematical Society)

Model Theory of $mathrm {C}^*$-Algebras (Memoirs of the American Mathematical Society)

Homological and Homotopical Aspects of Torsion Theories (Memoirs of the American Mathematical Society)

Directions in Mathematical Quasicrystals (CRM Monograph Series)

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in $mathbb {R}^n$ (Memoirs of the American Mathematical Society)

Knot Invariants and Higher Representation Theory (Memoirs of the American Mathematical Society)

Harmonic Analysis on Commutative Spaces (Mathematical Surveys & Monographs)

Axiomatic Stable Homotopy Theory (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

The Tiling Book: An Introduction to the Mathematical Theory of Tilings

A Random Tiling Model for Two Dimensional Electrostatics (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

A Theory of Generalized Donaldson-Thomas Invariants (Memoirs of the AMS) (Memoirs of the American Mathematical Society)

Springer Computational Invariant Theory: 130 Mathematics Book

The Local Structure of Algebraic K-Theory: 18 (Algebra and Applications, 18)

Topological Invariants of Stratified Spaces (Springer Monographs in Mathematics)

Geometry of Moduli Spaces and Representation Theory (IAS/Park City Mathematics Series)

Basic Algebraic Geometry (Springer Study Edition)

Global Aspects of Ergodic Group Actions (Mathematical Surveys and Monographs)

Rationality Problem for Algebraic Tori (Memoirs of the American Mathematical Society)

Cohomology of Groups and Algebraic K-theory (Advanced Lectures in Mathematics)

Covering Dimension of C*-Algebras and 2-Coloured Classification (Memoirs of the American Mathematical Society)

Affine Flag Varieties and Quantum Symmetric Pairs (Memoirs of the American Mathematical Society)

Princeton University Press - Equivariant Cohomology AMS-204

K3 Surfaces and Their Moduli: 315 (Progress in Mathematics, 315)