Local Index Formula on the Equatorial Podles Sphere

Abstract

We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one. After the identification of the smooth pre-$C^{\ast }$-algebra we compute the dimension spectrum and residues. We check the nontriviality of the (noncommutative) Chern character of the associated Fredholm modules by computing the pairing with the fundamental projector of the $C^{\ast }$-algebra (the nontrivial generator of the $K_0$-group) as well as the pairing with the $q$-analogue of the Bott projector. Finally, we show that the local index formula is trivially satisfied.

18 pages, no figures; minor corrections

References in corpus (5)

• The Dirac operator on SU_q(2)
• Local index formula for SU_q(2)
• Spectral triples and associated Connes-de Rham complex for the quantum SU(2) and the quantum sphere
• Geometry of Quantum Spheres
• Line bundles on quantum spheres

Cited by in corpus (11)

• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• Spectral dimensions and dimension spectra of quantum spacetimes
• Heat trace and spectral action on the standard Podles sphere
• Bounded and unbounded Fredholm modules for quantum projective spaces
• The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
• Spectral action on SU_q(2)
• Derivations and Spectral Triples on Quantum Domains I: Quantum Disk
• Dirac operators on all Podles quantum spheres
• The local index formula for quantum SU(2)
• Noncommutative Geometry and Quantum Group Symmetries
• A Note on Spectral Triples on the Quantum Disk