The real cycle class map
Algebraic Geometry
2021-08-25 v3 Algebraic Topology
K-Theory and Homology
Abstract
The classical cycle class map for a smooth complex variety sends cycles in the Chow ring to cycles in the singular cohomology ring. We study two cycle class maps for smooth real varieties: the map from the I-cohomology ring to singular cohomology induced by the signature, and a new cycle class map defined on the Chow-Witt ring. For both maps, we establish basic compatibility results like compatibility with pullbacks, pushforwards and cup products. As a first application of these general results, we show that both cycle class maps are isomorphisms for cellular varieties.
Cite
@article{arxiv.1911.04150,
title = {The real cycle class map},
author = {Jens Hornbostel and Matthias Wendt and Heng Xie and Marcus Zibrowius},
journal= {arXiv preprint arXiv:1911.04150},
year = {2021}
}
Comments
v3 various changes and additions