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19922023
most citedNon Commutative Geometry of Tilings and Gap Labelling

148 citations · 677 across the 41 of their papers we have counts for

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Showing cond-matShow all

4 papers · 1 filter

cond-mat1996★ 59 cited

Topological equivalence of tilings

Johannes Kellendonk

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 anot…

cond-mat1995★ 111 cited

The Local Structure of Tilings and their Integer Group of Coinvariants

Johannes Kellendonk

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…

cond-mat1995

On -Groups for Substitution Tilings

Johannes Kellendonk

The group $C(\Om,\Z)/\E$ is determined for tilings which are invariant under a locally invertible primitive \sst\ which forces its \saum. In case the tiling may be obtained by the…

cond-mat1994

Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings

Johannes Kellendonk

For a large class of tilings, including those which are obtained by the generalized dual method from regular grids, it is shown that their algebra is stably isomorphic to a crossed…