Related papers: Primitive du cocycle de Maslov g\'en\'eralis\'e

Given a $G$-toric, folded-symplectic manifold with co-orientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where $\frak{g}^*$ is the dual…

Combining geometric group theory techniques with geometric topology tools, we show how primitive cohomologies provide useful insights towards unifying the mathematical formulation of Gromov-Witten invariants. In particular, we emphasise the…

A wonderful compactification of an orbit under the action of a semi-simple and simply connected group is a smooth projective variety containing the orbit as a dense open subset, and where the added boundary divisor is simple normal…

We prove a geometric criterion on a $\SL$-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the Kontsevich--Zorich cocycle on the real…

The restricted $S$-matrix of $V^G$ is determined for any regular vertex operator algebra $V$ and finite automorphism group $G$ of $V.$ As an application, the $S$-matrices for cyclic permutation orbifolds of prime orders are computed.

From a view point of the moment map, we shall introduce the notion of Einstein-Hermitian generalized connections over a generalized K\"ahler manifold of symplectic type. We show that moduli spaces of Einstein-Hermitian generalized…

For each surface $S$ of genus $g>2$ we construct pairs of conjugate pseudo-Anosov maps, $\varphi_1$ and $\varphi_2$, and two non-equivalent covers $p_i: \tilde S \longrightarrow S$, $i=1,2$, so that the lift of $\varphi_1$ to $\tilde S$…

The standard (Berezin-Toeplitz) geometric quantization of a compact Kaehler manifold is restricted by integrality conditions. These restrictions can be circumvented by passing to the universal covering space, provided that the lift of the…

We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and…

In this paper, we first get a criterion formula for whether a differential form is holomorphic with respect to the generalized complex structure induced by $\epsilon$. Next, we get the local extensions of $\overline\partial$-closed forms on…

Under GRH, any element in the multiplicative group of a number field $K$ that is globally primitive (i.e., not a perfect power in $K^*$) is a primitive root modulo a set of primes of $K$ of positive density. For elliptic curves $E/K$ that…

In this paper, we explicitly express the local Maslov index by a Maslov index in finite dimensional case without symplectic reduction. Then we calculate the Maslov index for the path of pairs of Lagrangian subspaces in triangular form. In…

Let D be a central simple algebra of prime degree over a field and let E be an SL_1(D)-torsor. We determine the complete motivic decomposition of certain compactifications of E. We also compute the Chow ring of E.

We compute the generalized slices (as defined by Spitzweck-{\O}stv{\ae}r) of the motivic spectrum KO (representing hermitian K-theory) in terms of motivic cohomology and (a version of) generalized motivic cohomology, obtaining good…

Let $ l : \Sigma \to X$ be a weakly Lagrangian map of a compact orientable surface $ \Sigma$ in a K\"ahler surface $ X$ which is area minimizing in its homotopy class of maps in $ W^{1,2}(\Sigma, X)$, the Sobolev space of maps of square…

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…

Let $f: X \to S$ be a unipotent degeneration of projective complex manifolds over a disc such that the reduction of the central fibre $Y=f^{-1}(0)$ is simple normal crossings, and let $X_\infty$ be the canonical nearby fibre. Building on…

The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition…

Let H be a spherical subgroup of minimal rank of the semisimple simply connected complex algebraic group G. We define some functions on the homogeneous space G/H that we call generalised spherical minors. When G = H x H, we recover…

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold.…