Euler classes of vector bundles over manifolds

Authors

Aniruddha C. Naolekar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Mathematica Slovaca

Abstract

Let Ek denote the set of diffeomorphism classes of closed connected smooth k-manifolds X with the property that for any oriented vector bundle α over X, the Euler class e(α) = 0. We show that if X ∈ E2n+1 is orientable, then X is a rational homology sphere and π1(X) is perfect. We also show that E8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in Ek

First Page

199

Last Page

210

DOI

10.1515/ms-2017-0461

Publication Date

2-1-2021

Recommended Citation

Naolekar, Aniruddha C., "Euler classes of vector bundles over manifolds" (2021). Journal Articles. 2097.
https://digitalcommons.isical.ac.in/journal-articles/2097