Séminaire de Géométrie, Groupes et Dynamique

Marcos Cossarini: "Discrete Metric Geometry"

435 (UMPA)



A wallsystem on a manifold is a codimension-1 submanifold
satisfying certain conditions. It allows us to define a discrete
notion of length and volume: the length of a curve in the manifold is
the number of times that it crosses the wallsystem, and the volume of
the manifold (of dimension n) is the number of self-intersections of
order n of the wallsystem.  We will see how to approximate any
Riemannian metric on a compact manifold by a wallsystem, and we'll
discuss applications to the filling area problem and the inverse
problem for boundary distances.