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- J. Kellendonk
- 1995

To a given tiling a non commutative space and the corresponding Câˆ—-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. Theâ€¦ (More)

- J. Kellendonk
- 1997

The local structure of a tiling is described in terms of a multiplicative structure on its pattern classes. The groupoid associated to the tiling is derived from this structure and its integer groupâ€¦ (More)

- J. Kellendonk, Ian F. Putnam
- 2000

We describe the construction of Câˆ—-algebras from tilings. We describe the K-theory of such Câˆ—-algebras and discuss applications of these ideas in physics. We do not assume any familiarity withâ€¦ (More)

- J. Kellendonk
- 1997

We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show thatâ€¦ (More)

This memoir develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns,â€¦ (More)

- J. Kellendonk
- 2003

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a constructionâ€¦ (More)

We define the cohomology of a tiling as the cocycle cohomology of its associated groupoid and consider this cohomology for the class of tilings which are obtained from a higher dimensional lattice byâ€¦ (More)

The paper is a presentation of recent investigations on potential scattering in R. We advocate a new formula for the wave operators and deduce the various outcomes that follow from this formula. Aâ€¦ (More)

- J. Kellendonk, D. Lenz, Jean Savinien
- Discrete Mathematics
- 2013

We consider minimal, aperiodic symbolic subshifts and show how to characterize the combinatorial property of bounded powers by means of a metric property. For this purpose we construct a family ofâ€¦ (More)

- Tim Hoffmann, J. Kellendonk, Nadja Kutz, Nicolai Reshetikhin
- 2008

It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can beâ€¦ (More)