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The
real cycle class map
Jens Hornbostel, Matthias Wendt, Heng Xie and Marcus Zibrowius |
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Vol. 6 (2021), No. 2, 239–317
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Abstract |
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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 -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 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. |
Keywords
I-cohomology, singular cohomology, Chow–Witt rings, real
realization, real cellular varieties
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Mathematical Subject Classification 2010
Primary: 14F25
Secondary: 19G12
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Milestones
Received: 5 December 2019
Revised: 5 November 2020
Accepted: 22 November 2020
Published: 1 August 2021
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Authors |
| Jens Hornbostel | |
| Fachgruppe Mathematik und
Informatik Bergische Universität Wuppertal Wuppertal Germany |
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| Matthias Wendt | |
| Fachgruppe Mathematik und
Informatik Bergische Universität Wuppertal Wuppertal Germany |
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| Heng Xie | |
| Fachgruppe Mathematik und
Informatik Bergische Universität Wuppertal Wuppertal Germany |
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| Marcus Zibrowius | |
| Mathematisches Institut Heinrich Heine University Düsseldorf Düsseldorf Germany |
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