nLab Jean Bellissard

Jean Vincent Bellissard

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Selected writings

Early discussion of what much later become known as the K-theory classification of topological phases of matter:

• Jean Bellissard: K-theory of $C^\ast$-Algebras in solid state physics, in: Statistical mechanics and field theory: Mathematical Aspects, Lecture Notes in Physics 2577, Springer (1986) 99–156 [doi:10.1007/3-540-16777-3_74, inSpire:222243, scan:pdf]

and applied to quasicrystals via KK-theory of the noncommutative topology of quasiperiodicity:

• Jean Bellissard, The Noncommutative Geometry of Aperiodic Solids, in: Geometric and Topological Methods for Quantum Field Theory, pp. 86-156 (2003) (pdf, doi:10.1142/9789812705068_0002)

Discussion of the integer quantum Hall effect via a Brillouin torus with noncommutative geometry and using the Connes-Chern character:

• Jean Bellissard, A. van Elst, H. Schulz-Baldes: The noncommutative geometry of the quantum Hall effect, J. Math. Phys. 35 5373 (1994) [doi:10.1063/1.530758, cond-mat/9411052]

category: people