Conjugation Spaces are Cohomologically Pure
Algebraic Topology
2021-02-10 v3
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.
Cite
@article{arxiv.1908.03088,
title = {Conjugation Spaces are Cohomologically Pure},
author = {Wolfgang Pitsch and Nicolas Ricka and Jerome Scherer},
journal= {arXiv preprint arXiv:1908.03088},
year = {2021}
}
Comments
39 pages. This version corrected some misprints and a few misleading proofs