  Employing Morse theory for the global control of monodromy and the method of
analytic discs for local extension, we establish a version of the global
Hartogs extension theorem in a singular setting: for every domain D of an
(n-1)-complete normal complex space X of pure dimension n >= 2 and for every
compact set K in D such that D - K is connected, holomorphic or meromorphic
functions in D - K extend holomorphically or meromorphically to D. Normality is
an unvavoidable assumption for holomorphic extension, but we show that
meromorphic extension holds on a reduced globally irreducible (not necessarily
normal) X of pure dimension n >=2 provided that the regular part of D - K is
connected.
