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October, 2019 Proof of Kobayashi's rank conjecture on Clifford–Klein forms
Yosuke MORITA
J. Math. Soc. Japan 71(4): 1153-1171 (October, 2019). DOI: 10.2969/jmsj/78007800

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

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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

Information

Received: 18 May 2017; Revised: 29 May 2018; Published: October, 2019
First available in Project Euclid: 3 July 2019

zbMATH: 07174400
MathSciNet: MR4023301
Digital Object Identifier: 10.2969/jmsj/78007800

Subjects:
Primary: 57S30
Secondary: 17B56, 55P62, 57T15

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 4 • October, 2019
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