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# The fundamental group of a rigid Lagrangian cobordism

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### 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.

### Most cited references3

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### action

(1995)
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### The surgery of lagrange submanifolds

(1991)
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### Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents

(1991)
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### Author and article information

###### Journal
2017-02-08
###### Article
1702.02345