Abstract
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 $\operatorname{rank} G - \operatorname{rank} K < \operatorname{rank} H - \operatorname{rank} K_H$. 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.
Funding Statement
This work was supported by JSPS KAKENHI Grant Numbers 14J08233 and 17H06784, and the Program for Leading Graduate Schools, MEXT, Japan.
Citation
Yosuke MORITA. "Proof of Kobayashi's rank conjecture on Clifford–Klein forms." J. Math. Soc. Japan 71 (4) 1153 - 1171, October, 2019. https://doi.org/10.2969/jmsj/78007800
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