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Discovery Projects - Grant ID: DP130100490

Title
Discovery Projects - Grant ID: DP130100490
Funding
ARC | Discovery Projects
Contract (GA) number
DP130100490
Start Date
2013/01/01
End Date
2015/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP130100490

 

  • Dynamical correspondences for Smale spaces

    Deeley, Robin J.; Killough, D. Brady; Whittaker, Michael F. (2015)
    Projects: ARC | Discovery Projects - Grant ID: DP130100490 (DP130100490)
    We initiate the study of correspondences for Smale spaces. Correspondences are shown to provide a notion of a generalized morphism between Smale spaces and are a special case of finite equivalences. Furthermore, for shifts of finite type, a correspondence is related to a matrix which intertwines the adjacency matrices of the shifts. This observation allows us to define an equivalence relation on all Smale spaces which reduces to shift equivalence for shifts of finite type. Several other notio...

    Fractal spectral triples on Kellendonk's C*-algebra of a substitution tiling

    Mampusti, Michael; Whittaker, Michael F. (2017)
    Projects: ARC | Discovery Projects - Grant ID: DP130100490 (DP130100490)
    We introduce a new class of noncommutative spectral triples on Kellendonk's $C^*$-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that ...

    Wieler solenoids, Cuntz-Pimsner algebras and K-theory

    We study irreducible Smale spaces with totally disconnected stable sets and their associated $K$-theoretic invariants. Such Smale spaces arise as Wieler solenoids, and we restrict to those arising from open surjections. The paper follows three converging tracks: one dynamical, one operator algebraic and one $K$-theoretic. Using Wieler's Theorem, we characterize the unstable set of a finite set of periodic points as a locally trivial fibre bundle with discrete fibres over a compact space. This...
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