A canonical trace associated with certain spectral triples.
A de Rham theorem in the context of noncommutative geometry.
A new construction of characteristic classes for noncommutative algebraic principal bundles
We propose a new construction of characteristic classes for noncommutative algebraic principal bundles (Hopf-Galois extensions) with values in Hochschild and cyclic homology.
A note on flat noncommutative connections
It is proven that every flat connection or covariant derivative ∇ on a left A-module M (with respect to the universal differential calculus) induces a right A-module structure on M so that ∇ is a bimodule connection on M or M is a flat differentiable bimodule. Similarly a flat hom-connection on a right A-module M induces a compatible left A-action.
A Thom isomorphism for infinite rank Euclidean bundles.
A view on optimal transport from noncommutative geometry.
An idempotent for a Jordanian quantum complex sphere
A new Jordanian quantum complex 4-sphere together with an instanton-type idempotent is obtained as a suspension of the Jordanian quantum group .
Commutator representations of covariant differential calculi
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Différentielles non commutatives et théorie de Galois différentielle ou aux différences
Dirac operator on the standard Podleś quantum sphere
Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, reality structure J and the Dirac operator D, which has bounded commutators with the elements of the algebra and satisfies the first order condition.
Equilogical spaces, homology and non-commutative geometry
Equivariant spectral triples
We present the review of noncommutative symmetries applied to Connes' formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries: isospectral (twisted) deformations (including noncommutative torus) and finite spectral triples.
From Finsler geometry to noncommutative geometry.
Generalized signature operators and spectral triples for the Kronecker foliation
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.
Géométrie non commutative, opérateur de signature transverse et algèbres de Hopf
Global eikonal condition for Lorentzian distance function in noncommutative geometry.
Group -algebras as compact quantum metric spaces.
Heat trace asymptotics on noncommutative spaces.
Homotopy invariance of twisted higher signatures on manifolds with boundary