On trivialities of euler classes of oriented vector bundles over manifolds
Homology, Homotopy and Applications
We study manifolds on which all oriented bundles have trivial Euler class. In this note, we give a complete a characterization of such manifolds in dimension less than six, in terms of their cohomology groups, and obtain some partial results for manifolds of dimension 6.
Naolekar, Aniruddha C.; Subhash, B.; and Thakur, Ajay Singh, "On trivialities of euler classes of oriented vector bundles over manifolds" (2020). Journal Articles. 534.