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
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收藏
页码：199 / 210
页数：12
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