W-triviality of low dimensional manifolds

Authors

Aritra C. Bhattacharya, Michigan State University
Bikramjit Kundu, Indian Institute of Technology Roorkee
Aniruddha C. Naolekar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Manuscripta Mathematica

Abstract

A space X is W-trivial if for every real vector bundle α over X the total Stiefel-Whitney class w(α) is 1. It follows from a result of Milnor that if X is an orientable closed smooth manifold of dimension 1, 2, 4 or 8, then X is not W-trivial. In this note we completely characterize W-trivial orientable connected closed smooth manifolds in dimensions 3, 5 and 6. In dimension 7, we describe necessary conditions for an orientable connected closed smooth 7-manifold to be W-trivial.

First Page

499

Last Page

512

DOI

10.1007/s00229-024-01575-x

Publication Date

9-1-2024

Comments

Open Access; Green Open Access

Recommended Citation

Bhattacharya, Aritra C.; Kundu, Bikramjit; and Naolekar, Aniruddha C., "W-triviality of low dimensional manifolds" (2024). Journal Articles. 5195.
https://digitalcommons.isical.ac.in/journal-articles/5195