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Title: Proof of Kobayashi's rank conjecture on Clifford–Klein forms
Authors: Morita, Yosuke
Author's alias: 森田, 陽介
Keywords: Clifford–Klein form
pure Sullivan algebra
relative Lie algebra cohomology
transgression
Issue Date: Oct-2019
Publisher: Mathematical Society of Japan (Project Euclid)
Journal title: Journal of the Mathematical Society of Japan
Volume: 71
Issue: 4
Start page: 1153
End page: 1171
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 rankG−rankK<rankH−rankKH. 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.
Rights: © 2019 The Mathematical Society of Japan
The full-text file will be made open to the public on 1 October 2022 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
URI: http://hdl.handle.net/2433/244704
DOI(Published Version): 10.2969/jmsj/78007800
Appears in Collections:Journal Articles

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