2019/06/18 by Hisaaki Endo, Endo, Hisaaki, Andrei Pajitnov +1
Mathematics · #32J18 #32J27 #57R99 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1906.07401
openalex publication_date 2019/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct a family of complex analytic manifolds that generalize Inoue surfaces and Oeljeklaus-Toma manifolds. To a matrix M in SL(N,ℤ) satisfying some mild conditions on its characteristic polynomial we associate a manifold T(M,D) (depending on an auxiliary parameter D). This manifold fibers over the s-dimensional torus \mathbbTs, where s is the number of real eigenvalues of M. The fiber is the N-dimensional torus \mathbbTN, and the monodromy matrices are certain polynomials of the matrix M. The basic difference of our construction from the preceding ones is that we admit non-diagonalizable matrices M and the monodromy of the above fibration can also be non-diagonalizable. We prove that for a large class of non-diagonalizable matrices M the manifold T(M,D) does not admit any Kähler structure and is not homeomorphic to any of Oeljeklaus-Toma manifolds.