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Algebraic Cycles and the Classical Groups. Part 1. Real Cycles

机译：代数周期与古典群。第1部分。真实周期

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The groups of algebraic cycles on complex projective space P(V) are known to have211u001ebeautiful and suprising properties. Therefore, when V carries a real structure, 211u001eit is natural to ask for the properties of the groups of real algebraic cycles on 211u001eP(V). Similarly, if V carries a quaternionic structure, one can define 211u001equaternionic algebriac cycles and ask the same question. In this paper and its 211u001esequel the homotopy structure of these cycle groups is completely determined. It 211u001eturns out to be quite simple and to bear a direct relationship to characteristic 211u001eclasses for the classical groups. It is shown, moreover, that certain functors in 211u001eK-theory extend directly to these groups. It is shown, moreover, that certain 211u001efunctors in K-theory extend directly to these groups. It is also shown that, 211u001eafter taking colimits over dimension and codimension and codimension, the groups 211u001eof real and quaternionic cycles carry E(infinity)-ring structures, and that the 211u001emaps extending the K-theory functors are E(infinity)-ring maps. This gives a wide 211u001egeneralization of the results in (BLLMM) on the Segal question.

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