W-triviality of low dimensional manifolds

被引：0
|
作者：
Bhattacharya, Aritra C. [1 ]
Kundu, Bikramjit [2 ]
Naolekar, Aniruddha C. [3 ]
机构：
[1] Michigan State Univ, 619 Red Cedar Rd,Wells Hall, E Lansing, MI 48824 USA
[2] Indian Inst Technol, Dept Math, Haridwar Rd, Roorkee 247667, India
[3] Indian Stat Inst, Stat Math Unit, 8th Mile,Mysore Rd,RVCE Post, Bangalore 560059, India
来源：
MANUSCRIPTA MATHEMATICA | 2024年 / 175卷 / 1-2期
关键词：
57R20; VECTOR-BUNDLES; EULER CLASSES;
D O I：
10.1007/s00229-024-01575-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：499 / 512
页数：14
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