On $3$-connected $10$-dimensional manifolds
Hiroyasu Ishimoto · Proceedings of the Japan Academy Series A Mathematical Sciences · 1990
Introduction.In [4], the author gave a complete homotopy clas- sification of 2-connected smooth 8-manifolds with vanishing 4th homology groups as. an application of the homotopy classification theory of primary manifolds.In this pper, as nother pplication of it, we classify 3- connected smooth 10-manifolds M satisfying the following hypotheses:(H1) H(M) is torsion free.(H2) The tangent bundle of M is trivial on its 4-skeleton.It is easily seen that (H2) is equivalent to (H2') The tangent bundle of M is stably trivial.