Can I read $W$-triviality of low dimensional manifolds on EtoBox?

$W$-triviality of low dimensional manifolds by Bhattacharya, Aritra C; Kundu, Bikramjit; Naolekar, Aniruddha C is a scholarly article available to read on EtoBox.

What is $W$-triviality of low dimensional manifolds about?

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 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.

Author

Bhattacharya, Aritra C; Kundu, Bikramjit; Naolekar, Aniruddha C

Published

2023

Language

EN