相关论文: Two Gauss-Bonnet and Poincar\'{e}-Hopf Theorems fo…

For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…

We generalise gauge theory on a graph so that the gauge group becomes a finite-dimensional ribbon Hopf algebra, the graph becomes a ribbon graph, and gauge-theoretic concepts such as connections, gauge transformations and observables are…

In this paper we address the relation between the orbifold fundamental group and the topology of the underlying space. In particular, under the assumption that the orbifold fundamental group is equal to the fundamental group of the…

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (phi,Gamma)-module over the Robba ring; this is a variant of a result of Herr. We then…

On an oriented Riemannian manifold, the Gauss-Bonnet-Chern formula asserts that the Pfaffian of the metric represents, in de Rham cohomology, the Euler class of the tangent bundle. Hence, if the underlying manifold is compact, the integral…

The Grothendieck-Ogg-Shafarevich formula expresses the Euler characteristic of an etale sheaf on a curve in terms of local data. The purpose of this paper is to prove a version of the G-O-S formula which applies to equicharacteristic…

In this paper we study a family of generalizations of the Pontryagin and Husain-Kucha\v{r} actions on manifolds with boundary. In some cases, they describe well-known models---either at the boundary or in the bulk---such as 3-dimensional…

As an application of the Bochner formula, we prove that if a $2$-dimensional Riemannian manifold admits a non-trivial smooth tangent vector field $X$ then its Gauss curvature is the divergence of a tangent vector field, constructed from…

We establish a localized Bochner-type rigidity theorem for harmonic maps between Riemannian manifolds. Let $f : (M,g) \to (\overline{M},\overline{g})$ be a harmonic map from a compact manifold. Instead of assuming a global nonpositivity…

In this paper, we prove the following two results: First, we study a class of conformally invariant operators $P$ and their related conformally invariant curvatures $Q$ on even-dimensional Riemannian manifolds. When the manifold is locally…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

We show that the $\kappa$-Poincar\'e Hopf algebra can be interpreted in the framework of curved momentum space leading to the relativity of locality \cite{AFKS}. We study the geometric properties of the momentum space described by…

A domain $S\subset{\mathbb{R}}^d$ is said to fulfill the Poincar\'{e} cone property if any point in the boundary of $S$ is the vertex of a (finite) cone which does not otherwise intersects the closure $\bar{S}$. For more than a century,…

We consider a simple and natural coboundary operator, on the Lie algebra valued differential forms on a manifold, which in the abelian case reduces to usual exterior derivative of such forms. Using the corresponding de Rham cohomology Lie…

In this paper we introduce and study the basic properties of de Rham cohomology for a certain class of non-Hausdorff manifolds. After a careful discussion of non-Hausdorff differential forms, we provide a description of de Rham cohomology…

In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L^2-cohomology of these…

We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincar\'e duality theorem between homology and cohomology that preserves this structure.…

After analyzing renormalization schemes on a Poincar\'e-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian…

We prove a Hopf bifurcation theorem in general Banach spaces, which improves a classical result by Crandall and Rabinowitz. Actually, our theorem does not need any compactness conditions, which leads to wider applications. In particular,…

We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from…