Euler classes of vector bundles over manifolds-Reference-Cited by-同舟云学术

Euler classes of vector bundles over manifolds

Published:2021-01-29 Issue:1 Volume:71 Page:199-210
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Naolekar Aniruddha C.¹

Affiliation:

1. Statistics and Mathematics Unit, Indian Statistical Institute , 8th Mile Mysore Road, RVCE Post , Bangalore , India

Abstract

Abstract Let 𝓔 k 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 π 1(X) is perfect. We also show that 𝓔8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k .

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0461/pdf

Reference10 articles.

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3. Guijarro, L.—Schick, T.—Walschap, G.: Bundles with spherical Euler class, Pacific J. Math. 27(2) (2002), 377–392.

4. Hatcher, A.: Algebraic Topology, https://pi.math.cornell.edu/hatcher/AT/AT.pdf

5. Husemoller, D.: Fibre Bundles, Springer-Verlag, New York 1966.

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