Fractional quantum numbers, complex orbifolds and noncommutative geometry

Twisted Index Theory on Good Orbifolds, Ii: Fractional Quantum Numbers

This paper uses techniques in noncommutative geometry as developed by Alain Connes [Co2], in order to study the twisted higher index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group, continuing our earlier work [MM]. We also compute the range of the higher cyclic traces on K-theory...

Towards the Fractional Quantum Hall Effect: a Noncommutative Geometry Perspective

In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative geometry produced by the presence of a magnetic field. We recall how one can obtain this way a single electron model of the integer quantum Hall effect. While in th...

Quantum Groups and Noncommutative Geometry

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself powerful enough to make sense in the quantum domain. Just as the last century saw the birth of classical geometry, so the present century sees at its end the birt...

Noncommutative Geometry and Quantum Groups

Twisted Higher Index Theory on Good Orbifolds and Fractional Quantum Numbers

In this paper, we study the twisted higher index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group, and we apply these results to obtain qualitative results, related to generalizations of the Bethe-Sommerfeld conjecture, on the spectrum of self adjoint elliptic operators which are i...