A global spherical shell in a complex surface 
is a holomorphically embedded neighborhood
of the standard 3-sphere in 
whose complement in 
is connected. Thus there is an open
neighborhood 
of
 |
and a biholomorphism 
onto an open subset of 
, with 
connected. The embedding of a complex neighborhood and
the connectedness of its complement are part of the definition. This is a structure
on a complex surface, distinct from the Euclidean
region between two concentric spheres. It is central to the classification problem
for minimal class VII surfaces with positive
second Betti number.
