Abstract

Let $\pi:E\to M$ be a smooth fibre bundle where $E$ has the structure of a symplectic manifold and the fibres are Lagrangian submanifolds. Let $L\subset E$ be a Lagrangian submanifold generically transversal to the fibres of $\pi$. A point $x\in L$ is a singular point if the differential of the restriction of $\pi$ to $L$ fails to be surjective at $x$ in which case it is called a Lagrangian singularity. Lagrangian Singularities occur in problems of differential geometry and theoretical physics. Following the work of Entov et al., I will describe how certain Lagrangian singularities can be deformed into simpler ones through Hamiltonian deformations.



Information: