Conjugation spaces are cohomologically pure

Pitsch, Wolfgang; Ricka, Nicolas; Scherer, Jérôme

doi:10.1112/plms.12399

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Conjugation spaces are cohomologically pure

MPS-Authors

/persons/resource/persons236149

Scherer, Jérôme
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1112/plms.12399
(Publisher version)

https://doi.org/10.48550/arXiv.1908.03088
(Preprint)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Pitsch, W., Ricka, N., & Scherer, J. (2021). Conjugation spaces are cohomologically pure. Proceedings of the London Mathematical Society, 123(3), 313-344. doi:10.1112/plms.12399.

Cite as: https://hdl.handle.net/21.11116/0000-0009-8CA4-0

Abstract

Conjugation spaces are equipped with an involution such that the fixed points
have the same mod 2 cohomology (as a graded vector space, a ring, and even an
unstable algebra) but with all degrees divided by 2, generalizing the classical
examples of complex projective spaces under complex conjugation. Using tools
from stable equivariant homotopy theory we provide a characterization of
conjugation spaces in terms of purity. This conceptual viewpoint, compared to
the more computational original definition, allows us to recover all known
structural properties of conjugation spaces.