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Title: Euler characteristics and cohomology for quasiperiodic projection patterns
Authors: Irving, Claire Louise
Award date: 2006
Presented at: University of Leicester
Abstract: This thesis investigates quasiperiodic patterns and, in particular, polytopal projection patterns, which are produced using the projection method by choosing the acceptance domain to be a polytope. Cohomology theories applicable in this setting are defined, together with the Euler characteristic.;Formulae for the Cech cohomology Hˇ* ( M P ) and Euler characteristic eP are determined for polytopal projection patterns of codimension 2 and calculations are carried out for several examples. The Euler characteristic is shown to be undefined for certain codimension 3 polytopal projection patterns. The Euler characteristic eP is proved to be always defined for a particular class of codimension n polytopal projection patterns P and a formula for eP for such patterns is given. The finiteness or otherwise of the rank of Hˇm(M P ) ⊗ Q for m ≥ 0 is also discussed for various classes of polytopal projection patterns. Lastly, a model for M P is considered which leads to an alternative method for computing the rank of Hˇm(M P ) ⊗ Q for P a d-dimensional codimension n polytopal projection pattern with d > n..
Type: Thesis
Level: Doctoral
Qualification: PhD
Rights: Copyright © the author. All rights reserved.
Appears in Collections:Theses, Dept. of Mathematics
Leicester Theses

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