Singular manifolds

SINGULAR LAGRANGIAN MANIFOLDS and SEMI-CLASSICAL ANALYSIS

Lagrangian submanifolds of symplectic manifolds are very central objects in classical mechanics and microlocal analysis. These manifolds are frequently singular (integrable systems, bifurcations, reduction). There has been a lot of works on singular Lagrangian manifolds initiated by Arnold, Givental and others. The goal of our paper is to extend the classical and semi-classical normal forms of ...

Cartan’s structural equations for singular manifolds

The classical Cartan’s structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of singularities, we need to study the geometry of manifolds endowed on the tangent bundle with a symmetric bilinear form which is allowed to become degenerate. B...

A Note on the Singular Manifolds of a Difference Polynomial

Ads Manifolds with Particles and Earthquakes on Singular Surfaces

We prove an “Earthquake Theorem” for closed hyperbolic surfaces with cone singularities where the total angle is less than π: the action of the space of measured laminations on Teichmüller space by left earthquakes is simply transitive. This is strongly related to another result: the space of “globally hyperbolic” AdS manifolds with cone singularities (of given angle) along time-like geodesics ...

Locally toric manifolds and singular Bohr-Sommerfeld leaves

When geometric quantization is applied to a manifold using a real polarization which is “nice enough”, a result of Śniatycki says that the quantization can be found by counting certain objects, called BohrSommerfeld leaves. Subsequently, several authors have taken this as motivation for counting Bohr-Sommerfeld leaves when studying the quantization of manifolds which are less “nice”. In this pa...