Proof of Kobayashi's rank conjecture on Clifford-Klein forms

Yosuke Morita

doi:10.2969/jmsj/78007800

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arXiv · 1705.06544

Proof of Kobayashi's rank conjecture on Clifford-Klein forms

Yosuke Morita

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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.

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Yosuke Morita. 2017-05-18. Proof of Kobayashi's rank conjecture on Clifford-Klein forms. https://doi.org/10.2969/jmsj%2F78007800

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