$W$-triviality of low dimensional manifolds

Aritra C Bhattacharya, Bikramjit Kundu, Aniruddha C Naolekar

A space $X$ is $W$-trivial if for every real vector bundle $\alpha$ over $X$ the total Stiefel-Whitney class $w(\alpha )$ is 1. It follows from a result of Milnor that if $X$ is an orientable…