相关论文: On a Poincare lemma for foliations

We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…

We consider the problem of shadowing for differential equations with grow-up. We introduce so-called nonuniform shadowing properties (in which size of the error depends on the point of the phase space) and prove for them analogs of…

As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…

We show that the topological equivalence class of holomorphic foliation germs with an isolated singularity of Poincar\'e type is determined by the topological equivalence class of the real intersection foliation of the (suitably normalized)…

We consider holomorphic foliations by curves on compact complex manifolds, for which we investigate the existence of projective structures along the leaves varying holomorphically (foliated projective structures), that satisfy particular…

We enumerate complex algebraic hypersurfaces in $P^n$, of a given (high) degree with one singular point of a given singularity type. Our approach is to compute the (co)homology classes of the corresponding equi-singular strata in the…

In a previous paper, there was defined a multi-index filtration on the ring of functions on a hypersurface singularity corresponding to its Newton diagram generalizing (for a curve singularity) the divisorial one. Its Poincar\'e series was…

To a digraph with a choice of certain integral basis, we construct a CW complex, whose integral singular cohomology is canonically isomorphic to the path cohomology of the digraph as introduced in \cite{GLMY}. The homotopy type of the CW…

After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of…

A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the…

The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…

We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…

This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…

In this work, we construct some irreducible components of the space of two-dimensional holomorphic foliations on $\mathbb{P}^n$ associated to some algebraic representations of the affine Lie algebra $\mathfrak{aff}(\mathbb{C})$. We give a…

We consider nilmanifolds with left-invariant complex structure and prove that small deformations of such structures are again left invariant if the Dolbeault-cohomology of the nilmanifold can be calculated using left-invariant forms. By a…

We consider an integrable Hamiltonian system with n-degrees of freedom whose first integrals are invariant under the symplectic action of a compact Lie group G. We prove that the singular Lagrangian foliation associated to this Hamiltonian…

We prove the non-abelian Poincare lemma in higher gauge theory in two different ways. The first method uses a result by Jacobowitz which states solvability conditions for differential equations of a certain type. The second method extends a…

We give a formula for the Eisenstein cohomology of local systems on the partial compactification of the moduli of principally polarized abelian varieties given by rank 1 degenerations. For genus 2 we give a formula for the full Eisenstein…

In this expository article, we study and discuss invariants of vector fields and holomorphic foliations that intertwine the theories of complex analytic singular varieties and singular holomorphic foliations on complex manifolds: two…

Foliate systems are those which preserve some (possibly singular) foliation of phase space, such as systems with integrals, systems with continuous symmetries, and skew product systems. We study numerical integrators which also preserve the…