Algebraic cycles and the classical groups. I: real cycles

详细信息    查看全文

• 作者：Lawson ; H. Blaine ; Lima-Filho ; Paulo ; Michelsohn ; Marie-Louise
• 关键词：14C25 ; 55P43 ; 14P99 ; 19L99 ; 55P47 ; 55P91 ; Real algebraic cycles ; E_&infin ; -ring spectra ; Characteristic classes ; Equivariant infinite loop spaces ; KR-theory
• 刊名：Topology
• 出版年：2003
• 出版时间：March, 2003
• 年：2003
• 卷：42
• 期：2
• 页码：467-506
• 全文大小：392 K

文摘

The groups of algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real structure, it is natural to ask for the properties of the groups of real algebraic cycles on P(V). Similarly, if V carries a quaternionic structure, one can define quaternionic algebraic cycles and ask the same question. In this paper and its sequel the homotopy structure of these cycle groups is completely determined. It turns out to be quite simple and to bear a direct relationship to characteristic classes for the classical groups.