Related papers: Induced differential characters on nonlinear Gra{\…
Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of…
We use the theory of Berezin-Toeplitz operators of Ma and Marinescu to study the spaces of holomorphic sections of a prequantizing line bundle over compact K\"ahler manifolds under deformations of the complex structure. We show that the…
This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The…
We form real-analytic Eisenstein series twisted by Manin's noncommutative modular symbols. After developing their basic properties, these series are shown to have meromorphic continuations to the entire complex plane and satisfy functional…
For a Lie groupoid $G$, the differential forms on its nerve comprise a double complex. A natural question is if this statement extends to forms with values in a representation $V$ of $G$. In this paper, we research two types of covariant…
Let $f:X \to S$ be a Galois cover of Riemann surfaces, with Galois group $G$. In this paper we analyze the $G$-invariant divisors on $X$, and their associated spaces of meromorphic functions, differentials, and $q$-differentials. We…
On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
This paper is about non-Euclidean analysis on Lie groups endowed with left invariant distributions, seen as sub-Riemannian manifolds. This is a an updated version, which will be modified according to the contributions of the other…
We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on $T^*M$ is made into a space of (full) symbols of operators acting on forms on $M$. This gives rise to the composition of symbols,…
Using the higher covariant derivative on a manifold $ M $ equipped with a torsion-free connection, we define a natural surjective bundle map $ \Phi $ from $ (\otimes(TM))\otimes (\wedge(TM)) $ to the vector bundle $ \mathcal{U}(M) $ of de…
We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential…
We derive the couplings of noncommutative D-branes to spatially varying Ramond-Ramond fields, extending our earlier results in hep-th/0009101. These couplings are expressed in terms of *n products of operators involving open Wilson lines.…
In this paper we discuss how to associate a suitable non-transitive version of a Cartan connection to sub-Riemannian manifolds of corank 1 (including contact and quasi-contact sub-Riemannian manifolds) with non-necessarily constant…
Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…
We introduce a pre-symplectic structure on the space of connections in a G-principal bundle over a four-manifold and a Hamiltonian action on it of the group of gauge transformations that are trivial on the boundary. The moment map is given…
We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in…
Let $X$ be a compact K\"ahler manifold. The set $\cha(X)$ of one-dimensional complex valued characters of the fundamental group of $X$ forms an algebraic group. Consider the subset of $\cha(X)$ consisting of those characters for which the…
We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…
We give the complete classification of left-invariant sub-Riemannian structures on three dimensional Lie groups in terms of the basic differential invariants. This classifications recovers other known classification results in the…