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Cohomology in one-dimensional substitution tiling spaces
Author(s):
Marcy
Barge;
Beverly
Diamond
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2183-2191.
MSC (2000):
Primary 37B05;
Secondary 37A30, 37B50, 54H20
Posted:
February 19, 2008
MathSciNet review:
2383524
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Additional information
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.
References:
-
- [AP]
- J.E. Anderson and I.F. Putnam, Topological invariants for substitution tilings and their associated
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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:
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
Posted:
February 19, 2008
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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