Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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On the generalization of Inoue manifolds

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Andrei Pajitnov
Endo Hisaaki

Abstract

This paper is about a generalization of celebrated Inoue's surfaces. To each matrix M in SL(2n+1,ℤ) we associate a complex non-Kähler manifold TM of complex dimension n+1. This manifold fibers over S1 with the fiber T2n+1 and monodromy MT. Our construction is elementary and does not use algebraic number theory. We show that some of the Oeljeklaus-Toma manifolds are biholomorphic to the manifolds of type TM. We prove that if M is not diagonalizable, then TM does not admit a Kähler structure and is not homeomorphic to any of Oeljeklaus-Toma manifolds.


 

Keywords:
Inoue surface, monodromy, Kaehler structure

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How to Cite
Pajitnov, A., & Hisaaki, E. (2020). On the generalization of Inoue manifolds. Proceedings of the International Geometry Center, 13(4), 24-39. https://doi.org/10.15673/tmgc.v13i4.1748
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Papers
Author Biographies

Andrei Pajitnov, Laboratoire Mathematiques Jean Leray UMR 6629, Universite de Nantes, Faculte des Sciences, 2, rue de la Houssiniere, 44072, Nantes, Cedex

Laboratoire Mathematiques Jean Leray UMR 6629, Universite de Nantes, Faculte des Sciences, 2, rue de la Houssiniere, 44072, Nantes, Cedex

Endo Hisaaki, Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku Tokyo, 152-8551 Japan

Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku Tokyo, 152-8551 Japan