Related papers: Compactly supported analytic indices for Lie group…

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

Given a smooth and separated K(pi,1) variety X over a field k, we associate a "cycle class" in etale cohomology with compact supports to any continuous section of the natural map from the arithmetic fundamental group of X to the absolute…

We show that the category of internal groupoids in an exact Mal'tsev category is reflective, and in fact a Birkhoff subcategory of the category of simplicial objects. We then characterize the central extensions of the corresponding Galois…

We give a uniform construction of the higher indices of elliptic operators associated to Alexander-Spanier cocycles of either parity in terms of a pairing a la Connes between the K-theory and the cyclic cohomology of the algebra of complete…

We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…

We introduce a simplified (coarse) version of pseudo-differential calculus for operators of order zero on complete Riemannian manifolds. This calculus works for the usual Hormander (1,0) class of operators, as well as for…

We study Lie algebroids from the point of view noncommutative geometry. More specifically, using ideas from deformation quantization, we use the PBW-theorem for Lie algebroids to construct a Fedosov-type resolution for the associated…

In previous papers (arxiv:math/0612370 and arxiv:0909.1342) we defined the C*-algebra and the longitudinal pseudodifferential calculus of any singular foliation (M,F). Here we construct the analytic index of an elliptic operator as a…

Consider a Lie subalgebra $\mathfrak{l} \subset \mathfrak{g}$ and an $\mathfrak{l}$-invariant open submanifold $V \subset \mathfrak{l}^{\ast}$. We demonstrate that any smooth dynamical twist on $V$, valued in $U(\mathfrak{g}) \otimes…

We study multivariate generalisations of the classical Wiener--Hopf algebra, which is the C$^*$-algebra generated by the Wiener--Hopf operators, given by the convolutions restricted to convex cones. By the work of Muhly and Renault, this…

We construct a regularized index of a generalized Dirac operator on a complete Riemannian manifold endowed with a proper action of a unimodular Lie group. We show that the index is preserved by a certain class of non-compact cobordisms and…

We establish the compactly generated shape (H-shape) index theory for local semiflows on complete metric spaces via more general shape index pairs, and define the H-shape cohomology index to develop the Morse equations. The main advantages…

In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of…

Given a simple Lie group $G$, we show that the lattices in $G$ are weakly uniformly discrete. This is a strengthening of the Kazhdan-Margulis theorem. Our proof however is straightforward --- considering general IRS rather than lattices…

We upgrade the classical operation of \textit{isomonodromic deformations} along a path $\gamma$ to a functor $\mathbb{P}_{\gamma}$ between categories of flat connections with logarithmic singularities along a divisor $D$, which itself…

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

We have previously shown that the truncated Weil algebra of any Lie algebra is a Hopf-cyclic type complex with nontrivial coefficients. In this paper we apply this result to transfer the characteristic classes of transversely orientable…

We prove a {\Gamma}-equivariant version of the algebraic index theorem, where {\Gamma} is a discrete group of automorphisms of a formal deformation of a symplectic manifold. The particular cases of this result are the algebraic version of…

Taking a compact K\"{a}hler manifold as playground, we explore the powerfulness of Hodge index theorem. A main object is the Lorentzian classes on a compact K\"{a}hler manifold, behind which the characterization via Lorentzian polynomials…

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…