#
nLab

isotropic submanifold

### Context

#### Symplectic geometry

**symplectic geometry**

higher symplectic geometry

## Background

geometry

differential geometry

## Basic concepts

almost symplectic structure, metaplectic structure, metalinear structure

symplectic form, n-plectic form

symplectic Lie n-algebroid

symplectic infinity-groupoid

symplectomorphism, symplectomorphism group

Hamiltonian action, moment map

symplectic reduction, BRST-BV formalism

isotropic submanifold, Lagrangian submanifold, polarization

## Classical mechanics and quantization

Hamiltonian mechanics

quantization

deformation quantization,

**geometric quantization**, higher geometric quantization

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# Contents

## Definition

### Traditional definition

A submanifold of a symplectic manifold each tangent space of which is an isotropic subspace with respect to the ambient symplectic structure is an **isotropic submanifold**.

Last revised on March 18, 2013 at 23:51:22.
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