5 papers
A topological version of Levinson's theorem
Johannes Kellendonk, Serge Richard
In the framework of scattering theory, we show how the scattering matrix can be related to the projection on the bound states by an index map of K-theory. Pairings with appropriate…
Universal groups for point-sets and tilings
Johannes Kellendonk, Mark V Lawson
We study the universal groups of inverse semigroups associated with point sets and with tilings. We focus our attention on two classes of examples. The first class consists of poin…
Cohomology groups for projection point patterns
Alan Forrest, John Hunton, Johannes Kellendonk
Aperiodic point sets (or tilings) which can be obtained by the method of cut and projection from higher dimensional periodic sets play an important role for the description of quas…
Topological invariants for projection method patterns
Alan Forrest, John Hunton, Johannes Kellendonk
We analyze and compare different dynamical systems and groupoids which can be obtained from projection point patterns. We define the cohomology of a point pattern as the cocycle co…
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…