EULER CLASSES OF VECTOR BUNDLES OVER MANIFOLDS

被引：1

作者：

Naolekar, Aniruddha C. ^{[1
]}

机构：

[1] Indian Stat Inst, Stat & Math Unit, 8th Mile Mysore Rd,RVCE Post, Bangalore, Karnataka, India

来源：

MATHEMATICA SLOVACA | 2021年 / 71卷 / 01期

关键词：

Euler class; rational homology sphere;

D O I：

10.1515/ms-2017-0461

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 alpha over X, the Euler class e(alpha) = 0. We show that if X is an element of E2n+1 is orientable, then X is a rational homology sphere and pi(1)(X) is perfect. We also show that E-8 = empty set and derive additional cohomlogical restrictions on orientable manifolds in E-k. (C) 2021 Mathematical Institute Slovak Academy of Sciences

引用

页码：199 / 210

页数：12

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