Wayne State University
Mathematics Department
Topology Seminar
Jean Bellissard
Université Paul Sabatier, Toulouse,
France
Tuesday, December 5, 2000
FAB 1285
The Gap Labeling Theorem for 3D Aperiodic Solids
We will review the notions of Hull of an
Aperiodic Solid, of Non Commutative Brillouin Zone (NCBZ) and of the electronic
Density of States. We will address the problem of labeling the gap of the electronic
spectrum. We will show how this is related to the K-theory of the NCBZ. Then we
will establish a conjecture for solids with transversally Cantor Hull. We will
review the results obtained previously in dimension d=1,2. Then we will give
the proof of the conjecture in d=3. We will use a spectral sequence to solve
this problem.