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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.

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            The surgery of lagrange submanifolds

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              Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents

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                Author and article information

                Journal
                2017-02-08
                Article
                1702.02345

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                math.SG

                Geometry & Topology

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