A note on stable complex structures on real vector bundles over manifolds

被引：3

作者：

Yang, Huijun ^{[1
]}

机构：

[1] Henan Univ, Sch Math & Stat, Kaifeng 475004, Henan, Peoples R China

来源：

TOPOLOGY AND ITS APPLICATIONS | 2015年 / 189卷

基金：

中国国家自然科学基金;

关键词：

Stable complex structure; Real reduction; Atiyah-Hirzebruch spectral sequence; Differentiable Riemann-Roch theorem;

D O I：

10.1016/j.topol.2015.03.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be an n-dimensional closed oriented smooth manifold with n equivalent to 0 mod 8, xi be a real vector bundle over M. Suppose that xi admits a stable complex structure over the (n 1)-skeleton of M. Then the necessary and sufficient conditions for xi to admit a stable complex structure over M are given in terms of the characteristic classes of xi and M. As an application, we obtain the criteria to determine which real vector bundle over 8-dimensional manifold admits a stable complex structure. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：1 / 9

页数：9

共 4 条

[1] A REMARK ON THE STABLE REAL FORMS OF COMPLEX VECTOR BUNDLES OVER MANIFOLDS
Yang, Huijun
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2017, 96 (01) : 69 - 76
[2] On the classification of complex vector bundles of stable rank
Banica, Constantin
Putinar, Mihai
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2006, 116 (03): : 271 - 291
[3] On the classification of complex vector bundles of stable rank
Constantin Banica
Mihai Putinar
Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2006, 116 : 271 - 291
[4] Almost complex structures on (n-1)-connected 2n-manifolds
Yang, Huijun
TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (05) : 1361 - 1368

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