Summary: TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 219, 1976
SIMPLICIALTRIANGULATION OF NONCOMBINATORIAL
MANIFOLDS OF DIMENSION LESS THAN 9
ABSTRACT. Necessary and sufficient conditions are given for the sim-
plicial triangulation of all noncombinatorial manifolds in the dimension range
5 < n < 7, for which the integral Bockstein of the combinatorial triangulation
obstruction is trivial. A weaker theorem is proven in case n = 8.
The appendix contains a proof that a map between PL manifolds which
is a TOP fiber bundle can be made a PL fiber bundle.
0. Two of the oldest and most difficult problems arising in manifold
theory are the following:
(i) Is every manifold homeomorphic to a simplicial complex?
(ii) Is every simplicia1triangulation of a manifold combinatorial (i.e. must
the link of every simplex be a sphere)?
Among the consequences of the fundamental breakthrough of Kirby-