Journal of Symplectic Geometry

Volume 3 (2005)

Number 4

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

Pages: 565 – 587



Robert E. Gompf


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 ${\le}2$.

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