https://card-file.onaft.edu.ua/handle/123456789/6192 geom-center.onaft.edu.ua Sun, 20 Mar 2022 04:26:01 GMT 2022-03-20T04:26:01Z https://card-file.onaft.edu.ua/handle/123456789/16682 Title: On the generalization of Inoue manifolds Authors: 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.
   Wed, 01 Jan 2020 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/16682 2020-01-01T00:00:00Z https://card-file.onaft.edu.ua/handle/123456789/16680 Title: Floer-Novikov cohomology and symplectic fixed points, revisited Authors: Kaoru Ono, Hong Van Le Abstract: This note is mostly an exposition of a few versions of Floer-Novikov cohomology with a few new observations. For example, we state a lower bound for the number of symplectic fixed points of a non-degenerate symplectomorphism, which is symplectomorphic isotopic to the identity, on a compact symplectic manifold, more precisely than previous statements in [14,10]. Wed, 01 Jan 2020 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/16680 2020-01-01T00:00:00Z https://card-file.onaft.edu.ua/handle/123456789/16681 Title: Olympic links in a Chebotarev link Authors: Jun Ueki Abstract: The Chebotarev law for an infinite link is an equidistribution property about how its components are linked in a group theoretic sense. We overview several properties of a Chebotarev link following the author's article "Chebotarev links are stable generic". In addition, we exhibit the density of modulo 2 Olympic links in a Chebotarev link. Wed, 01 Jan 2020 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/16681 2020-01-01T00:00:00Z https://card-file.onaft.edu.ua/handle/123456789/16679 Title: On Rham cohomology of locally trivial Lie groupoids over triangulated manifolds Authors: Jose R. Oliveira Abstract: Based on the isomorphism between Lie algebroid cohomology and piecewise smooth cohomology of a transitive Lie algebroid, it is proved that the Rham cohomology of a locally trivial Lie groupoid G on a smooth manifold M is isomorphic to the piecewise Rham cohomology of G, in which G and M are manifolds without boundary and M is smoothly triangulated by a finite simplicial complex K such that, for each simplex ∆ of K, the inverse images of ∆ by the source and target mappings of G are transverses submanifolds in the ambient space G. As a consequence, it is shown that the piecewise de Rham cohomology of G does not depend on the triangulation of the base. Wed, 01 Jan 2020 00:00:00 GMT https://card-file.onaft.edu.ua/handle/123456789/16679 2020-01-01T00:00:00Z