相关论文: Residue Formulas for logarithmic Foliations and ap…
We study Poisson-flat connections with logarithmic poles along a simple normal crossings divisor on a holomorphic Poisson manifold, where flatness is required only along the symplectic foliation. After identifying the relevant logarithmic…
Given a cooriented branched surface $\mathcal B$ fully carrying a foliation $\mathcal F$, we use the dual graph of $\mathcal B$ to define a simplicial 1-cycle $\Gamma_m(\mathcal B)$ representing the Poincar\'e dual of the Euler class of…
An involutive distribution $C$ on a smooth manifold $M$ is a Lie-algebroid acting on sections of the normal bundle $TM/C$. It is known that the Chevalley-Eilenberg complex associated to this representation of $C$ possesses the structure…
Let E be a circle-equivariant complex-orientable cohomology theory. We show that the fixed-point formula applied to the free loopspace of a manifold X can be understood as a Riemann-Roch formula for the quotient of the formal group of E by…
We prove an explicit formula for the Poincar\'e polynomials of parabolic character varieties of Riemann surfaces with semisimple local monodromies, which was conjectured by Hausel, Letellier and Rodriguez-Villegas. Using an approach of…
We study the non-linear Dirichlet-to-Neumann map for the Poincar\'e-Einstein filling problem. For even dimensional manifolds the range of this non-local map is described in terms of a rank two "Dirichlet-to Neumann tensor" along the…
We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on…
We give a solution to the Poincar\'e Problem, in the formulation of Cerveau and Lins Neto. We obtain a bound on the degree of general leaves of foliations of general type, which is linear in $g$. To achieve this we study the birational…
We give complete geometric invariants of cobordisms of framed fold maps. These invariants consist of two types. We take the immersion of the fold singular set into the target manifold together with information about non-triviality of the…
A Generalized Inoue--Bombieri (GIB) manifold $M$ is a compact quotient of a connected Riemannian product $\mathbb{R}^q \times (N,g _N)$ by a discrete subgroup of $\mathrm{Sim}(\mathbb{R}^q) \times \mathrm{Isom}(N,g_N)$. The flat factor…
Esnault-Viehweg developed the theory of cyclic branched coverings $\tilde X\to X$ of smooth surfaces providing a very explicit formula for the decomposition of $H^1(\tilde X,\mathbb{C})$ in terms of a resolution of the ramification locus.…
Let X be a smooth compact manifold with boundary. For smooth foliations on the boundary of X admitting a `resolution' in terms of a fibration, we construct a pseudodifferential calculus generalizing the fibred cusp calculus of Mazzeo and…
In this article, we introduce the logarithmic de Rham stack of a pair (X, D), for a smooth variety X over a field k of positive characteristic p, and D a strict normal crossings divisor on X. Using this stack, we prove a new version of…
For a compact differentiable surface with boundary embedded in $\Bbb R^3$, we give simple proofs of the Gauss-Bonnet theorem, Poincar\'{e}-Hopf theorem, and several other integral formulas. We complete all of the proofs without using…
Let $\mathcal{F}$ be a singular codimension one holomorphic foliation on a compact complex manifold $X$ of dimension at least three such that its singular set has codimension at least two. In this paper, we determine Lehmann-Suwa residues…
We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.
Given a finite subset $F$ of integer points in $\mathbb Z^d$, it is of interest to seek conditions on $F$ that allow it to multi-tile $\mathbb Z^d$ by translations. To this end, we give a discretized version of the Bombieri-Siegel formula,…
A parallel lightlike vector field on a Lorentzian manifold $X$ naturally defines a foliation $\mathcal{F}$ of codimension one. If either all leaves of $\mathcal{F}$ are compact or $X$ itself is compact admitting a compact leaf and the…
We construct a foliation of an asymptotically flat end of a Riemannian manifold by hypersurfaces which are critical points of a natural functional arising in potential theory. These hypersurfaces are perturbations of large coordinate…
In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the \textit{schematization functor} $X \mapsto (X\otimes \mathbb{C})^{sch}$,…