# nLab surface

### Context

#### Manifolds and cobordisms

manifolds and cobordisms

# Contents

## Idea

A surface is a space of dimension 2.

In differential geometry this means a 2-dimensional smooth manifold or something thereby parametrized?.

In complex analytic geometry this usually means a complex manifold of complex dimension 2.

Similarly and more generally, in algebraic geometry an algebraic surface is a variety of algebraic dimension 2.

Revised on May 31, 2014 07:21:41 by Urs Schreiber (89.204.135.200)