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|Title:||Euler characteristics and cohomology for quasiperiodic projection patterns|
|Authors:||Irving, Claire Louise|
|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 ) âŠ— Q for m â‰¥ 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 ) âŠ— Q for P a d-dimensional codimension n polytopal projection pattern with d > n..|
|Rights:||Copyright © the author. All rights reserved.|
|Appears in Collections:||Theses, Dept. of Mathematics|
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