On certain triangulated manifolds
Masahisa Adachi · Proceedings of the Japan Academy Series A Mathematical Sciences · 1960
defined the combin- atorial Pontrjagin classes of triangulated manifolds and proved the existence of triangulated 8-dimensional manifolds which admit no differentiable structures compatible" with their given triangulations.A corresponding result for triangulated 16-dimensional manifolds was proved by K. Srinivasacharyulu [6.The purpose of this note is to prove the corresponding theorems for the dimensions of the form 4k (2k14, k 3).In 1 certain triangulated 4k-dimensional manifolds are constructed and studied.In 2 the theorem is proved.Our method is quite analogous to that of R. Thom, and closely related with J. Milnor [4.The word n-manifold will always be used for a compact oriented n-dimensional manifold without boundary.The word "differentiable" will be used to mean "differentiable of class C''.