A note on the characteristic rank of oriented Grassmann manifolds

被引：6

作者：

Rusin, Tomas ^{[1
]}

机构：

[1] Comenius Univ, Fac Math Phys & Informat, Dept Algebra Geometry & Math Educ, Bratislava 84248, Slovakia

来源：

TOPOLOGY AND ITS APPLICATIONS | 2017年 / 216卷

关键词：

Stiefel-Whitney class; Characteristic rank; Grassmann manifold; Cup-length; CUP-LENGTH;

D O I：

10.1016/j.topol.2016.11.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive new lower bound for the characteristic rank of the canonical 3-plane bundle (gamma) over tilden,3 over the oriented Grassmann manifold (G) over tilde (n,3) congruent to SO(n)/(SO(3) x SO(n - 3)) for all n in range 2(t)+2(t-1) <= n <= 2(t+1)- 4, t >= 3. Using this knowledge we determine the Z(2)-cup-length of (G) over tilde2(t)+2(t-1)+1,3 and (G) over tilde2(t)-F2t-1+2,3, verifying the corresponding claim of T. Fukaya's conjecture. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：48 / 58

页数：11

共 10 条

[1]

Borel A., 1953, Comment. Math. Helvetici, V27, P165, DOI [10.1007/BF02564561, DOI 10.1007/BF02564561]

[2] GROBNER BASES OF ORIENTED GRASSMANN MANIFOLDS [J].