M. C. Romero Fuster

The Horospherical Geometry of Submanifolds in Hyperbolic Space

We study some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic

Fold Maps from the Sphere to the Plane

n

On the number of singularities, zero curvature points and vertices of a simple convex space curve

-space as an application of the theory of Legendrian singularities.

Conformal curvatures of curves in

Any stable map from a surface to the plane has an associated graph. In the case of the sphere, such graphs are of tree type [Hacon et al. 03]. We characterize the trees that can occur as graphs of fold maps from the sphere to the plane. In order to do so, we first determine the sets of integers that may occur as winding numbers for the branch sets of these maps.

Global topological invariants of stable maps from 3-manifolds to ℝ3

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

Stable maps from surfaces to the plane with prescribed branching data

Abstract We define a complete set of conformal invariants for pairs of spheres in and obtain from these the expressions of the conformal curvatures of curves in (n + 1)-space in terms of the Euclidean invariants.

Topological Invariants of Stable Maps from a Surface to the Plane from a Global Viewpoint

With any stable map from a 3-manifold to ℝ3, we associate a graph with weights in its vertices and edges. These graphs are A-invariants from a global viewpoint. We study their properties and show that any tree with zero weights in its vertices and aleatory weights in its edges can be the graph of a stable map from S 3 to ℝ3.