{c}

A clean Lagrangian intersection is a <clean intersection> between two local Lagrangian sheets. A small exact perturbation of one sheet near a compact clean component replaces the intersection by the critical points of a <Morse function> on that component.


Clean Lagrangian intersection

Submanifolds $A,B\subseteq M$ intersect cleanly when $A\cap B$ is an <embedded submanifold> and
$$
T_x(A\cap B)=T_xA\cap T_xB
$$
at every $x\in A\cap B$. A <transverse intersection> is the special case in which $T_xA+T_xB=T_xM$.


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 Incoming links: Clean intersection