流形与Stiefel－Whitney类

Manifolds and Stiefel-Whitney classes

这篇短文将证明；在特殊情况下，如果不为零的Ｓｔｉｅｆｅｌ－Ｗｈｉｔｎｅｙ类的最高维数不超过该流形维数的二进表示中１的个数，则该流形必协边于零．

Let M be a smooth colsed manifold with dimension 2α0+ 2αl,where αc,α1 are integers and 0 ≤αc < α1. In this note we prove that if its total Stiefel--whitney class W =1 + W1 + W2,then [M ]2= 0.