Formality for algebroid stacks
We extend the formality theorem of M. Kontsevich from deformations of the structure sheaf on a manifold to deformations of gerbes.
math.QA↗
arXiv subjects
Alexander Gorokhovsky
Publications and source records attributed to Alexander Gorokhovsky.
Deformations of algebroid stacks
In this paper we consider deformations of an algebroid stack on an etale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.
math.QA↗
Chern character for twisted complexes
We construct a Chern character of a perfect complex of twisted modules over an algebroid stack.
math.KT↗
Local index theory over foliation groupoids
We give a superconnection proof of an index theorem for a Dirac-type operator that is invariant with respect to the action of a foliation groupoid.
math.DG↗
Bivariant Chern character and the longitudinal index theory
In this paper we consider a family of Dirac-type operators on fibration $P \to B$ equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant $K$ theory. We compute the action of the bivariant Chern character of this element on the image of Connes' map $Φ$ in the cyclic cohomology. A particular case of this result is Connes' index theorem for etale groupoids in the case of fibrations.
math.DG↗
Local Index Theory over Etale Groupoids
We give a superconnection proof of Connes' index theorem for proper cocompact actions of etale groupoids. This includes Connes' general foliation index theorem for foliations with Hausdorff holonomy groupoid.
math.DG↗
Secondary Characteristic Classes and Cyclic Cohomology of Hopf Algebras
We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.
math.OA↗
Characters of Cycles, Equivariant Characteristic Classes and Fredholm Modules
We derive simple explicit formulas for the character of a cycle in the Connes' (b,B)-bicomplex of cyclic cohomology and give applications to the Fredholm modules and equivariant characteristic classes.
math.DG↗
Chern Classes in Alexander-Spanier Cohomology
In this article we construct explicit cocycles in the Alexander-Spanier cohomological complex, representing the Chern character of an element in K-theory.
math.KT↗