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arXiv · 1911.04150

The real cycle class map

Jens Hornbostel·Matthias Wendt·Heng Xie·Marcus Zibrowius
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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.

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Jens Hornbostel, Matthias Wendt, Heng Xie, Marcus Zibrowius. 2020-11-25. The real cycle class map. https://doi.org/10.2140/akt.2021.6.239

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