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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cohomology in one-dimensional substitution tiling spaces


Authors: Marcy Barge and Beverly Diamond
Journal: Proc. Amer. Math. Soc. 136 (2008), 2183-2191
MSC (2000): Primary 37B05; Secondary 37A30, 37B50, 54H20
Published electronically: February 19, 2008
MathSciNet review: 2383524
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Abstract: Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which ``forces its border.'' One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomorphism induced by inflation and substitution on the cohomology of the complex. For one-dimensional substitution tiling spaces, we describe a modification of the Anderson-Putnam complex on collared tiles that allows for easier computation and provides a means of identifying certain special features of the tiling space with particular elements of the cohomology.


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Additional Information

Marcy Barge
Affiliation: Department of Mathematics, Montana State University, Bozeman, Montana 59717
Email: barge@math.montana.edu

Beverly Diamond
Affiliation: Department of Mathematics, College of Charleston, Charleston, South Carolina 29424
Email: diamondb@cofc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09225-3
PII: S 0002-9939(08)09225-3
Received by editor(s): February 14, 2007
Received by editor(s) in revised form: May 4, 2007
Published electronically: February 19, 2008
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.