Related papers: Higher Lefschetz formulas on {\Gamma}-proper manif…

In his approach to analytic number theory C. Deninger has suggested that to the Riemann zeta function $\hat{\zeta}(s)$ (resp. the zeta function $\zeta_Y(s)$ of a smooth projective curve $Y$ over a finite field $\mathbb{F}_q$, $q=p^f$)) one…

We study cocycles of countable groups $\Gamma$ of Borel automorphisms of a standard Borel space $(X, \mathcal{B})$ taking values in a locally compact second countable group $G$. We prove that for a hyperfinite group $\Gamma$ the subgroup of…

It is well-known that the study of proper affine isometric actions of countable discrete groups in various spaces plays a crucial role in geometric group theory, operator algebras, and high-dimensional topology. In this article, we shall…

We study an index of a transversal Dirac operator on an odd-dimensional manifold $X$ with locally free $\mathbb{S}^1$-action. One difficulty of using heat kernel method lies in the understanding of the asymptotic expansion as $t\to 0^+$. By…

We prove a Godbillon-Vey index formula for longitudinal Dirac operators on a foliated bundle with boundary; in particular, we define a Godbillon-Vey eta invariant on the boundary-foliation; this is a secondary invariant for longitudinal…

A *-product compatible with the comultiplication of the Hopf algebra of the functions on the Heisenberg group is determined by deforming a coboundary Lie-Poisson structure defined by a classical r-matrix satisfying the modified Yang-Baxter…

Integral symplectic 4-manifolds may be described in terms of Lefschetz fibrations. In this note we give a formula for the signature of any Lefschetz fibration in terms of the second cohomology of the moduli space of stable curves. As a…

For a torsion-free virtually polycyclic group $\Gamma$, we give a canonical homomorphism form certain finite-dimensional cochain complex to the $\Q$-polynomial de Rham complex of the simplicial classifying space $B\Gamma$ which induces a…

Let $G$ be a complex simply connected semisimple Lie group and let $\Gamma$ be a torsionless uniform irreducible lattice in $G$. Then $\Gamma\backslash G$ is a compact complex non-K\"ahler manifold whose tangent bundle is holomorphically…

The geometry of nonholonomic bundle gerbes, provided with nonlinear connection structure, and nonholonomic gerbe modules is elaborated as the theory of Clifford modules on nonholonomic manifolds which positively fail to be spin. We explore…

Higher index of signature operator is a far reaching generalization of signature of a closed oriented manifold. When two closed oriented manifolds are homotopy equivalent, one can define a secondary invariant of the relative signature…

Let $\Gamma$ be a fuchsian subgroup of \pslr. In this paper we consider the $\Gamma$-equivariant form of the Berezin's quantization of the upper half plane which will correspond to a deformation quantization of the (singular) space $\Bbb…

Let $\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\Gamma$ act on the geodesic boundary $\partial X$ of $X$. Via general constructions in…

Let M be a compact manifold with a fixed spin structure \chi. The Atiyah-Singer index theorem implies that for any metric g on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending…

For a closed cocompact subgroup $\Gamma$ of a locally compact group $G$, given a compact abelian subgroup $K$ of $G$ and a homomorphism $\rho:\hat{K}\to G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant…

We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function.…

In this article, we describe a computational study of the action of the two natural $U$-operators acting on $\Gamma$-invariant spaces of harmonic cocycles for $\mathrm{GL}_3$ for certain congruence subgroups $\Gamma$, in a positive…

We study finite group actions on smooth manifolds of the form $M\#\Sigma$, where $\Sigma$ is an exotic $n$-sphere and $M$ is a closed aspherical space form. We give a classification result for free actions of finite groups on $M\#\Sigma$…

We prove a cyclic cohomological analogue of Haefliger's van Est-type theorem for the groupoid of germs of diffeomorphisms of a manifold. The differentiable version of cyclic cohomology is associated to the algebra of transverse differential…

Let $\Gamma$ be a discrete finitely presented group. Pick any system $S$ of generators in $\Gamma$. In Cayley graph $\mathrm{Cay}(\Gamma)=\mathrm{Cay}(\Gamma, S)$ with edge set $E$, glue with oriented polygons all the group relations…