Proof of Kobayashi's rank conjecture on Clifford-Klein forms
Geometric Topology
2019-08-01 v2 Algebraic Topology
Abstract
T. Kobayashi conjectured in the 36th Geometry Symposium in Japan (1989) that a homogeneous space G/H of reductive type does not admit a compact Clifford-Klein form if rank G - rank K < rank H - rank K_H. We solve this conjecture affirmatively. We apply a cohomological obstruction to the existence of compact Clifford-Klein forms proved previously by the author, and use the Sullivan model for a reductive pair due to Cartan-Chevalley-Koszul-Weil.
Keywords
Cite
@article{arxiv.1705.06544,
title = {Proof of Kobayashi's rank conjecture on Clifford-Klein forms},
author = {Yosuke Morita},
journal= {arXiv preprint arXiv:1705.06544},
year = {2019}
}
Comments
21 pages, Introduction rewritten, presentation improved, to appear in J. Math. Soc. Japan