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 $L,L^{\prime }\subset (M,\omega )$. We show that under natural conditions the inclusions $L,L^{\prime }\hookrightarrow W$ induce surjective maps ${\pi }_1(L)\twoheadrightarrow {\pi }_1(W)$, ${\pi }_1(L^{\prime })\twoheadrightarrow {\pi }_1(W)$ and when the previous maps are injective then $W$ is an h-cobordism.

References in corpus (3)

• Quantum Structures for Lagrangian Submanifolds
• The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory
• Exact Lagrangian cobordism and pseudo-isotopy