Algebraic cycles and the classical groups II: Quaternionic cycles
摘要
In part I of this work we studied the spaces of real algebraic cycles on a complex projective space P(V), where V carries a real structure, and completely determined their homotopy type. We also extended some functors in K-theory to algebraic cycles, establishing a direct relationship to characteristic classes for the classical groups, specially Stiefel-Whitney classes. In this sequel, we establish corresponding results in the case where V has a quaternionic structure. The determination of the homotopy type of quaternionic algebraic cycles is more involved than in the real case, but has a similarly simple description. The stabilized space of quaternionic algebraic cycles admits a nontrivial infinite loop space structure yielding, in particular, a delooping of the total Pontrjagin class map. This stabilized space is directly related to an extended notion of quaternionic spaces and bundles (KH-theory), in analogy with Atiyah's real spaces and KR-theory, and the characteristic classes that we introduce for these objects are nontrivial. The paper ends with various examples and applications.
引用
@article{arxiv.math/0507451,
title = {Algebraic cycles and the classical groups II: Quaternionic cycles},
author = {H Blaine Lawson and Paulo Lima-Filho and Marie-Louise Michelsohn},
journal= {arXiv preprint arXiv:math/0507451},
year = {2014}
}
备注
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper27.abs.html