A local index formula for the quantum sphere

DOI10.1007/s00220-004-1154-zzbMath1079.58021arXivmath/0309275OpenAlexW1964669590MaRDI QIDQ2571114

Lars Tuset, Sergey V. Neshveyev

Publication date: 31 October 2005

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309275

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Exotic index theories on manifolds (58J22) Noncommutative geometry (à la Connes) (58B34) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (25)

The Dirac operator on \(\text{SU}_{q}(2)\) ⋮ Twisted Homology of Quantum SL(2) - Part II ⋮ An invariant for homogeneous spaces of compact quantum groups ⋮ Gauged Laplacians on quantum Hopf bundles ⋮ The Podleś spheres converge to the sphere ⋮ An analogue of Weyl’s law for quantized irreducible generalized flag manifolds ⋮ Twisted cyclic homology of all Podleś quantum spheres ⋮ Connes-Landi deformation of spectral triples ⋮ Dimensional reduction over the quantum sphere and non-Abelian \(q\)-vortices ⋮ Heat trace and spectral action on the standard Podleś sphere ⋮ The Dirac operator on compact quantum groups ⋮ The spectral geometry of the equatorial Podleś sphere ⋮ Gromov-Hausdorff convergence of quantised intervals ⋮ THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM PROJECTIVE PLANE ⋮ Twisted sigma-model solitons on the quantum projective line ⋮ The Podleś sphere as a spectral metric space ⋮ Regularity of twisted spectral triples and pseudodifferential calculi ⋮ Twisted cyclic theory, equivariant KK-theory and KMS states ⋮ On the noncommutative spin geometry of the standard Podleś sphere and index computations ⋮ Examples of gauged Laplacians on noncommutative spaces ⋮ Local index formulae on noncommutative orbifolds and equivariant zeta functions for the affine metaplectic group ⋮ Geometry of quantum spheres ⋮ A residue formula for the fundamental Hochschild class on the Podleś sphere ⋮ Non-commutative integration, zeta functions and the Haar state for \(\mathrm{SU}_q(2)\) ⋮ Asymptotic and exact expansions of heat traces

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