Related papers: Map drawing and foliations of the sphere
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…
We prove that the foliated Euler caracteristic classifies amenable measured foliations up to those defined by ergodic actions of the euclidian plane.
We present bijections for planar maps with boundaries. In particular, we obtain bijections for triangulations and quadrangulations of the sphere with boundaries of prescribed lengths. For triangulations we recover the beautiful factorized…
This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…
Mobiles are a particular class of decorated plane trees which serve as codings for planar maps. Here we address the question of enumerating mobiles in their most general flavor, in correspondence with planar Eulerian (i.e., bicolored) maps.…
We introduce bijections between families of rooted maps with unfixed genus and families of so-called blossoming trees endowed with an arbitrary forward matching of their leaves. We first focus on Eulerian maps with controlled vertex…
The action of the mapping class group of a surface on the collection of homotopy classes of disjointly embedded curves or arcs in the surface is discussed here as a tool for understanding Riemann's moduli space and its topological and…
The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The…
Schanuel has pointed out that there are mathematically interesting categories whose relationship to the ring of integers is analogous to the relationship between the category of finite sets and the semi-ring of non-negative integers. Such…
In this thesis we consider a discretization of the Euler top given by Hirota und Kimura. Using the geometric description of the conserved quantities as quadrics in real 3-space, we find that there exist maps on rulings of quadrics in the…
The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented. Some applications are given; in particular, a geometric…
A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees…
We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms…
This paper has three parts. The first part is a general introduction to rigidity and to rigid actions of mapping class group actions on various spaces. In the second part, we describe in detail four rigidity results that concern actions of…
This paper presents an analysis on the effects of floating-point arithmetic on the constructing bifurcation diagram of the quadratic map. More precisely, we are interested in showing the dependence of initial conditions to obtain some…
We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is…
We investigate several topics of triangle geometry in the elliptic and in the extended hyperbolic plane, such as: centers based on orthogonality, centers related to circumcircles and incircles, radical centers and centers of similitude,…
Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due…
The volume of a k-dimensional foliation $\mathcal{F}$ in a Riemannian manifold $M^{n}$ is defined as the mass of image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing a…
This paper provides the generating series for the embedding of tree-like graphs of arbitrary number of vertices, accourding to their genus. It applies and extends the techniques of Chan, where it was used to give an alternate proof of the…