# nLab Lagrangian cobordism

Contents

## Theorems

#### Symplectic geometry

symplectic geometry

higher symplectic geometry

# Contents

## Idea

A Lagrangian cobordism is roughly a cobordism between Lagrangian submanifolds which is itself a Lagrangian submanifold in a suitable sense.

More in detail, given an ambient symplectic manifold $(X, \omega)$, a Lagrangian cobordism in $X$ is a cobordism with an embedding into $([0,1] \times \mathbb{R} \times X )$ as a Lagrangian submanifold (where $[0,1] \times \mathbb{R} \hookrightarrow \mathbb{R}^2$ is equipped with its canonical symplectic structure) and such that the boundary components are Lagrangian submanifolds of $X$. (for details see e.g. Biran-Cornea 11, 2.1.1).

Lagrangian cobordisms in $(X,\omega)$ arrange into a stable (infinity,1)-category which is supposed to be at least closely related to the Fukaya category of $(X,\omega)$ (Nadler-Tannaka 11).

## References

The notion was introduced in

Further developments are in

A stable (infinity,1)-category of Lagrangian cobordisms is discussed in

Last revised on November 10, 2013 at 10:52:11. See the history of this page for a list of all contributions to it.