Homology, Homotopy and Applications

Volume 22 (2020)

Number 1

On trivialities of Euler classes of oriented vector bundles over manifolds

Pages: 215 – 232

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n1.a13


Aniruddha C. Naolekar (Stat-Math Unit, Indian Statistical Institute, Bangalore, India)

B. Subhash (Indian Institute of Science Education and research (IISER), Tirupati, India)

Ajay Singh Thakur (Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India)


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 $6$.


Euler class

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