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

被引：1

作者：

Morita, Yosuke ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Sci, Dept Math, Sakyo Ku, Kitashirakawa Oiwake Cho, Kyoto 6068502, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2019年 / 71卷 / 04期

关键词：

Clifford-Klein form; pure Sullivan algebra; relative Lie algebra cohomology; transgression; HOMOGENEOUS SPACES; PROPER ACTIONS; EXISTENCE;

D O I：

10.2969/jmsj/78007800

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1153 / 1171

页数：19