nLab
complex analytic topology

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Complex geometry

Contents

Idea

The analytic topology on an complex analytic space is the one given by covering the space by affine opens equipped with the standard topology induced from that of the complex numbers n\mathbb{C}^n.

Properties

Riemann existence theorem

Comparison theorem

Chow's theorem states that a projective complex analytic variety, hence a closed analytic subspace of a complex projective space, is also an algebraic variety over the complex numbers. In general this is not true.

The comparison theorem (étale cohomology) relates the étale cohomology of a complex variety with the ordinary cohomology of its complex analytic topological space.

For more along such lines see at GAGA.

References

Last revised on October 24, 2014 at 18:41:14. See the history of this page for a list of all contributions to it.