### Cohomology of one-dimensional mixed substitution tiling spaces

Gähler F, Maloney GR (2013)
Topology And Its Applications 160(5): 703-719.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Gähler, FranzUniBi; Maloney, Gregory R.
Einrichtung
Abstract / Bemerkung
We compute the Cech cohomology with integer coefficients of one-dimensional tiling spaces arising from not just one, but several different substitutions, all acting on the same set of tiles. These calculations involve the introduction of a universal version of the Anderson-Putnam complex. We show that, under a certain condition on the substitutions, the projective limit of this universal Anderson-Putnam complex is isomorphic to the tiling space, and we introduce a simplified universal Anderson-Putnam complex that can be used to compute Cech cohomology. We then use this simplified complex to place bounds on the rank of the first cohomology group of a one-dimensional substitution tiling space in terms of the number of tiles. (C) 2013 Elsevier B.V. All rights reserved.
Stichworte
Cohomology; Tiling spaces; Substitution
Erscheinungsjahr
2013
Zeitschriftentitel
Topology And Its Applications
Band
160
Ausgabe
5
Seite(n)
703-719
ISSN
0166-8641
Page URI
https://pub.uni-bielefeld.de/record/2578612

### Zitieren

Gähler F, Maloney GR. Cohomology of one-dimensional mixed substitution tiling spaces. Topology And Its Applications. 2013;160(5):703-719.
Gähler, F., & Maloney, G. R. (2013). Cohomology of one-dimensional mixed substitution tiling spaces. Topology And Its Applications, 160(5), 703-719. doi:10.1016/j.topol.2013.01.019
Gähler, F., and Maloney, G. R. (2013). Cohomology of one-dimensional mixed substitution tiling spaces. Topology And Its Applications 160, 703-719.
Gähler, F., & Maloney, G.R., 2013. Cohomology of one-dimensional mixed substitution tiling spaces. Topology And Its Applications, 160(5), p 703-719.
F. Gähler and G.R. Maloney, “Cohomology of one-dimensional mixed substitution tiling spaces”, Topology And Its Applications, vol. 160, 2013, pp. 703-719.
Gähler, F., Maloney, G.R.: Cohomology of one-dimensional mixed substitution tiling spaces. Topology And Its Applications. 160, 703-719 (2013).
Gähler, Franz, and Maloney, Gregory R. “Cohomology of one-dimensional mixed substitution tiling spaces”. Topology And Its Applications 160.5 (2013): 703-719.

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