On the Hirzebruch-Kobayashi-Ono proportionality principle and the non-existence of compact solvable Clifford-Klein forms of certain homogeneous spaces

Maciej Bochenski; Aleksy Tralle

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arXiv · 1705.03221

On the Hirzebruch-Kobayashi-Ono proportionality principle and the non-existence of compact solvable Clifford-Klein forms of certain homogeneous spaces

Maciej Bochenski·Aleksy Tralle

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Abstract

This article continues a line of research aimed at solving an important problem of T. Kobayashi of the existence of compact Clifford-Klein forms of reductive homogeneous spaces. We contribute to this topic by showing that almost all symmetric spaces and 3-symmetric spaces do not admit solvable compact CliffordfKlein forms (with several possible exceptions). Our basic tool is a combination of the Hirzebruch-Kobayashi-Ono proportionality principle with the theory of syndetic hulls. Using this, we prove a general theorem which yields a sufficient condition for the non-existence of compact solvable CliffordKlein forms.

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Maciej Bochenski, Aleksy Tralle. 2019-09-19. On the Hirzebruch-Kobayashi-Ono proportionality principle and the non-existence of compact solvable Clifford-Klein forms of certain homogeneous spaces. https://arxiv.org/abs/1705.03221

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