Related papers: Common zeros of inward vector fields on surfaces

We construct the space of vector fields on quantum groups . Its elements are products of the known left invariant vector fields with the elements of the quantum group itself. We also study the duality between vector fields and 1-forms. The…

We study the displacement map associated to small one-parameter polynomial unfoldings of polynomial Hamiltonian vector fields on the plane. Its leading term, the generating function $M(t)$, has an analytic continuation in the complex plane…

We prove an index theorem for boundary value problems in Boutet de Monvel's calculus on a compact manifold X with boundary. The basic tool is the tangent semigroupoid $\cT^-X$ generalizing the tangent groupoid defined by Connes in the…

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized…

In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. In the class of nonsmooth systems, that do not present sliding regions, a Poincar\'e-Bendixson Theorem is presented. A minimal set in…

Any traversally generic vector flow on a compact manifold $X$ with boundary leaves some residual structure on its boundary $\d X$. A part of this structure is the flow-generated causality map $C_v$, which takes a region of $\d X$ to the…

We introduce the notion of fundamental heap for compact orientable surfaces with boundary embedded in $3$-space, which is an isotopy invariant of the embedding. It is a group, endowed with a ternary heap operation, defined using diagrams of…

The disk complex of a surface in a 3-manifold is used to define its {\it topological index}. Surfaces with well-defined topological index are shown to generalize well-known classes, such as incompressible, strongly irreducible, and critical…

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf's result to topological manifolds, replacing…

Let $(X,0)$ be an isolated complete intersection complex singularity ($X$ can also be smooth at 0). Let $K$ be its link, $\cal X$ its canonical contact structure and $\D_X$ the complex vector bundle associated to $\cal X$. We prove that the…

If E(z,s) is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z,s) has a "Siegel zero." That is E(z,\beta)=0 for a real number \beta just to the left of one. We give a generalization of this…

The structural bifurcation of a 2D divergence free vector field $\mathbf{u}(\cdot, t)$ when $\mathbf{u}(\cdot, t_0)$ has an interior isolated singular point $\mathbf{x}_0$ of zero index has been studied by Ma and Wang. Although in the class…

Let $k$ be an algebraically closed field. The generalized or $n$-Kronecker quiver $K(n)$ is the quiver with two vertices, called a source and a sink, and $n$ arrows from source to sink. Given a finite-dimensional module $M$ of the path…

The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to…

We analyze the obstruction to metrics of positive scalar curvature within a given bounded distortion class of metrics. This obstruction lives in a non-Hausdorff cohomology group Poincare dual to the uniformly finite homology studied by…

Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,Z) is such a group. The main result of this paper is that every action of…

Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…

Let (K,v) be a valued field, Y a K-variety, G an algebraic group over K (not necessarily smooth), and f: X->Y a G-torsor over Y. We consider the induced map X(K)-->Y(K), which is continuous for the topologies deduced from the valuation. Let…

The aim of this paper is to explore the possibilities of Conley index techniques in the study of heteroclinic connections between finite and infinite invariant sets. For this, we remind the reader of the Poincar\'e compactification: this…

The paper presents a first step towards a family index theorem for classical self-adjoint boundary value problems. We address here the simplest non-trivial case of manifolds with boundary, namely the case of two-dimensional manifolds. The…