|
|||||
 |
|
|
|
The
real cycle class map
Jens Hornbostel, Matthias Wendt, Heng Xie and Marcus Zibrowius |
|
Vol. 6 (2021), No. 2, 239–317
|
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 -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. |
PDF Access Denied
We have not been able to recognize your IP address
18.97.9.173
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
I-cohomology, singular cohomology, Chow–Witt rings, real
realization, real cellular varieties
|
Mathematical Subject Classification 2010
Primary: 14F25
Secondary: 19G12
|
Milestones
Received: 5 December 2019
Revised: 5 November 2020
Accepted: 22 November 2020
Published: 1 August 2021
|
Authors |
| Jens Hornbostel | |
| Fachgruppe Mathematik und
Informatik Bergische Universität Wuppertal Wuppertal Germany |
|
| Matthias Wendt | |
| Fachgruppe Mathematik und
Informatik Bergische Universität Wuppertal Wuppertal Germany |
|
| Heng Xie | |
| Fachgruppe Mathematik und
Informatik Bergische Universität Wuppertal Wuppertal Germany |
|
| Marcus Zibrowius | |
| Mathematisches Institut Heinrich Heine University Düsseldorf Düsseldorf Germany |
|
