Page 1

Displaying 1 – 14 of 14

Showing per page

Generalized signature operators and spectral triples for the Kronecker foliation

R. Matthes, O. Richter, G. Rudolph (2003)

Banach Center Publications

We consider two spectral triples related to the Kronecker foliation. The corresponding generalized Dirac operators are constructed from first and second order signature operators. Furthermore, we consider the differential calculi corresponding to these spectral triples. In one case, the calculus has a description in terms of generators and relations, in the other case it is an "almost free" calculus.

K-theory of Boutet de Monvel's algebra

Severino T. Melo, Ryszard Nest, Elmar Schrohe (2003)

Banach Center Publications

We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).

Marcinkiewicz spaces, commutators and non-commutative geometry


Banach Center Publications

Nigel J. Kalton was one of the most eminent guests participating in the Józef Marcinkiewicz Centenary Conference. His contribution to the scientific aspect of the meeting was very essential. Nigel was going to prepare a paper based on his plenary lecture. The editors are completely sure that the paper would be a real ornament of the Proceedings. Unfortunately, Nigel's sudden death totally destroyed editors' hopes and plans. Every mathematician knows how unique were Nigel's mathematical achievements....

Quantum isometries and group dual subgroups

Teodor Banica, Jyotishman Bhowmick, Kenny De Commer (2012)

Annales mathématiques Blaise Pascal

We study the discrete groups Λ whose duals embed into a given compact quantum group, Λ ^ G . In the matrix case G U n + the embedding condition is equivalent to having a quotient map Γ U Λ , where F = { Γ U U U n } is a certain family of groups associated to G . We develop here a number of techniques for computing F , partly inspired from Bichon’s classification of group dual subgroups Λ ^ S n + . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...

Traces and quasi-traces on the Boutet de Monvel algebra

Gerd Grubb, Elmar Schrohe (2004)

Annales de l’institut Fourier

We construct an analogue of Kontsevich and Vishik’s canonical trace for pseudodifferential boundary value problems in the Boutet de Monvel calculus on compact manifolds with boundary. For an operator A in the calculus (of class zero), and an auxiliary operator B , formed of the Dirichlet realization of a strongly elliptic second- order differential operator and an elliptic operator on the boundary, we consider the coefficient C 0 ( A , B ) of ( - λ ) - N in the asymptotic expansion of the resolvent trace Tr ( A ( B - λ ) - N ) (with N large)...

Triplets spectraux pour les variétés à singularité conique isolée

Jean-Marie Lescure (2001)

Bulletin de la Société Mathématique de France

Sur une pseudo-variété de dimension paire à une singularité conique isolée, des triplets spectraux sont construits à partir d’une classe d’opérateurs différentiels elliptiques de type Fuchs, contenant les opérateurs de Dirac à coefficients dans des fibrés plats dans la direction radiale. Ces derniers engendrent, sous une hypothèse raisonnable, le groupe de K -homologie pair tensorisé par de la pseudo-variété et leur caractère de Chern est calculé.

Trivial noncommutative principal torus bundles

Stefan Wagner (2011)

Banach Center Publications

A (smooth) dynamical system with transformation group ⁿ is a triple (A,ⁿ,α), consisting of a unital locally convex algebra A, the n-torus ⁿ and a group homomorphism α: ⁿ → Aut(A), which induces a (smooth) continuous action of ⁿ on A. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of trivial principal ⁿ-bundles based on such dynamical systems, i.e., we call a dynamical system (A,ⁿ,α) a trivial noncommutative principal ⁿ-bundle if each isotypic component...

κ-deformation, affine group and spectral triples

Bruno Iochum, Thierry Masson, Andrzej Sitarz (2012)

Banach Center Publications

A regular spectral triple is proposed for a two-dimensional κ-deformation. It is based on the naturally associated affine group G, a smooth subalgebra of C*(G), and an operator 𝓓 defined by two derivations on this subalgebra. While 𝓓 has metric dimension two, the spectral dimension of the triple is one. This bypasses an obstruction described in [35] on existence of finitely-summable spectral triples for a compactified κ-deformation.

Currently displaying 1 – 14 of 14

Page 1