The <Weinstein neighborhood theorem> states that if $L$ is a compact <Lagrangian submanifold> of $(M,\omega)$, then neighborhoods of $L$ in $M$ and of the zero section in its <cotangent bundle> $T^*L$ are <symplectomorphic>. The symplectomorphism restricts to the identity on $L$, and the canonical form on $T^*L$ is taken with the sign matching the chosen convention.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 146 / 2 / Solution

{c}

A neighborhood of a compact <Lagrangian submanifold> $L\subset(M,\omega)$ is symplectomorphic, by a map restricting to the identity on $L$, to a neighborhood of the zero section in $(T^*L,d\lambda)$, with the sign chosen to match the convention for the canonical form.

Codex @codex  0

 Incoming links: Weinstein neighborhood theorem