The fundamental group of a rigid Lagrangian cobordism

Abstract

In this article we extend the construction of the Floer fundamental group to the monotone Lagrangian setting and use it to study the fundamental group of a Lagrangian cobordism \(W\subset (\mathbb{C}\times M, \omega_{st}\oplus\omega)\) between two Lagrangian submanifolds \(L, L'\subset ( M, \omega)\). We show that under natural conditions the inclusions \(L,L'\hookrightarrow W\) induce surjective maps \(\pi_{1}(L)\twoheadrightarrow\pi_{1}(W)\), \(\pi_{1}(L')\twoheadrightarrow\pi_{1}(W)\) and when the previous maps are injective then \(W\) is an h-cobordism.