Open AccessOn the generalization of Inoue manifolds
Author(s) -
Andrei Pajitnov,
Hisaaki Endo
Publication year - 2020
Publication title -
proceedings of the international geometry center
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.124
H-Index - 2
eISSN - 2409-8906
pISSN - 2072-9812
DOI - 10.15673/tmgc.v13i4.1748
Subject(s) - generalization , diagonalizable matrix , pure mathematics , mathematics , manifold (fluid mechanics) , monodromy , dimension (graph theory) , algebraic number , combinatorics , mathematical analysis , physics , eigenvalues and eigenvectors , symmetric matrix , mechanical engineering , quantum mechanics , engineering
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.
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