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The Bulletin of the London Mathematical Society, 1997-01, Vol.29 (1), p.98-102
Ort / Verlag
Cambridge University Press
Erscheinungsjahr
1997
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
The purpose of this note is to obtain
a restriction on the fundamental groups of
non-elliptic compact complex surfaces of class VII
in Kodaira's classification [9]. We
recall that these are the compact complex surfaces
with first Betti number one and no
non-constant meromorphic functions. This seems to be
the class of compact complex
surfaces whose structure is least understood. The first
and simplest examples are the
general Hopf surfaces [9, III]. Then there are various
classes of examples found by
Inoue [5, 6], and which have been studied in more
detail in [11]. The only known
topological restriction beyond the first Betti number
is that intersection form in two-dimensional
homology is negative definite. There seems
to be little known as to how
wide this class of surfaces is. We prove the
following theorem.