A topological necessary condition for the existence of compact Clifford-Klein forms

Autor:	Morita, Yosuke
Rok vydání:	2013
Předmět:	Mathematics - Differential Geometry Mathematics - Group Theory Mathematics - Geometric Topology Primary 57S30 Secondary 57T15 57R20 53C30 22E40
Zdroj:	J. Differential Geom. 100 (2015), 533-545
Druh dokumentu:	Working Paper
DOI:	10.4310/jdg/1432842364
Popis:	We provide a necessary condition for the existence of a compact Clifford-Klein form of a given homogeneous space of reductive type. The key to the proof is to combine a result of Kobayashi-Ono with an elementary fact that certain two different Clifford-Klein forms have the same cohomology ring. We give some examples, SL(p+q, R)/SO(p, q) (p, q: odd) for instance, of homogeneous spaces which do not admit compact Clifford-Klein forms. Comment: 16 pages, revised following referee's comments, to appear in Journal of Differential Geometry
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1310.7096 Zobrazit plný text záznamu View this record from Arxiv