Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-09-18T18:06:13.714Z Has data issue: false hasContentIssue false
  • English
  • Français

Augmented dimension groups and ordered cohomology

Published online by Cambridge University Press:  01 February 2009

MARCY BARGE  and
MEGAN SMITH
MARCY BARGE
Affiliation:
Department of Mathematics, Montana State University, Bozeman, MT 59717, USA (email: umsfmbar@math.montana.edu)
MEGAN SMITH
Affiliation:
Department of Mathematics, Montana State University, Bozeman, MT 59717, USA (email: umsfmbar@math.montana.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that the ordered Matsumoto K0-group of a substitutive system is derivable from the ordered Čech cohomology of a simple ‘augmentation’ of the tiling space associated with the substitution. Besides supplying a topological interpretation of the Matsumoto K0-group, this leads to finer invariants of the flow equivalence class of a substitutive system.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 1 , February 2009 , pp. 1 - 35
Copyright
Copyright © 2008 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Anderson, J. and Putnam, I.. Topological invariants for substitution tilings and their associated C *-algebras. Ergod. Th. & Dynam. Sys. 18(3) (1998), 509–537.CrossRefGoogle Scholar
[2]Barge, M. and Diamond, B.. A complete invariant for the topology of one-dimensional substitutive tiling spaces. Ergod. Th. & Dynam. Sys. 21(5) (2001), 1333–1358.Google Scholar
[3]Barge, M., Diamond, B. and Holton, C.. Asymptotic orbits of primitive substitutions. Theoret. Comput. Sci. 301 (2003), 439–450.CrossRefGoogle Scholar
[4]Barge, M., Jacklitch, J. and Vago, G.. Homeomorphisms of one-dimensional inverse limits with applications to substitution tilings, unstable manifolds, and tent maps. Contemp. Math. 246 (1999), 1–15.CrossRefGoogle Scholar
[5]Barge, M. and Swanson, R.. New techniques for classifying Williams solenoids. Tokyo J. Math. 30 (2007), 139–157.CrossRefGoogle Scholar
[6]Carlsen, T. and Eilers, S.. Augmenting dimension group invariants for substitution dynamics. Ergod. Th. & Dynam. Sys. 24(4) (2004), 1015–1039.Google Scholar
[7]Carlsen, T. and Eilers, S.. Matsumoto K-groups associated to certain shift spaces. Doc. Math. 9 (2004), 639–671.CrossRefGoogle Scholar
[8]Carlsen, T. and Eilers, S.. A graph approach to computing nondeterminacy in substitutional dynamical systems. RAIRO—Theoret. Inform. Appl. 41 (2007), 285–306.Google Scholar
[9]Carlsen, T. and Eilers, S.. Ordered K-groups associated to substitutional dynamics. J. Funct. Anal. 38 (2006), 99–117.Google Scholar
[10]Giordano, T., Putnam, I. and Skau, C.. Topological orbit equivalence and C *-crossed products. J. Reine Angew. Math. 469 (1995), 51–111.Google Scholar
[11]Matsumoto, K.. Bowen–Franks groups as an invariant for flow equivalence of subshifts. Ergod. Th. & Dynam. Sys. 21(6) (2001), 1831–1842.Google Scholar
[12]Williams, R. F.. One-dimensional non-wandering sets. Topology 6 (1967), 473–487.CrossRefGoogle Scholar
[13]Williams, R. F.. Classification of one-dimensional attractors. Proc. Sympos. Pure Math. 14 (1970), 341–361.CrossRefGoogle Scholar