Homology, Homotopy and Applications
Volume 22 (2020)
On trivialities of Euler classes of oriented vector bundles over manifolds
Pages: 215 – 232
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 $6$.
2010 Mathematics Subject Classification
The research of third author is partially supported by DST-Inspire Faculty research grant (IFA-13-MA-26).
Received 28 December 2018
Received revised 8 July 2019
Accepted 12 July 2019
Published 20 November 2019