## Journal of Symplectic Geometry

### Stein surfaces as open subsets of $\boldsymbol{\mathbb{C}}^2$

Robert E. Gompf

#### Abstract

An open subset $U$ of a complex surface can be topologically perturbed to yield an open subset whose inherited complex structure is Stein, if and only if $U$ is homeomorphic to the interior of a handlebody whose handles all have index ${\le}2$.

#### Article information

Source
J. Symplectic Geom., Volume 3, Number 4 (2005), 565-587.

Dates
First available in Project Euclid: 1 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1154467630

Mathematical Reviews number (MathSciNet)
MR2235855

Zentralblatt MATH identifier
1118.32011

#### Citation

Gompf, Robert E. Stein surfaces as open subsets of $\boldsymbol{\mathbb{C}}^2$. J. Symplectic Geom. 3 (2005), no. 4, 565--587. https://projecteuclid.org/euclid.jsg/1154467630