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Anosov diffeomorphisms on nilmanifolds
Proceedings of the American Mathematical Society, 1973The purpose of this paper is to give necessary conditions on the map induced by an Anosov diffeomorphism of a nilmanifold on its fundamental group.
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Compact locally conformal K�hler nilmanifolds
Geometriae Dedicata, 1986A generalized Hopf manifold is a locally conformal Kähler manifold whose Lee form is parallel but not exact [\textit{I. Vaisman}, Geom. Dedicata 13, 231--255 (1982; Zbl 0506.53032)]. The main non-Kähler example of such a manifold is \(S^1\times S^{2k+1}\), \(k\geq 1\).
Cordero, Luis A. +2 more
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1992
The author uses the techniques of rational homotopy theory to prove that for a nilmanifold \(M\), we have: \(\dim M=\text{rank}(\pi_ 1(M))=\text{cat}(M)=e_ 0(M)\). Here \(e_ 0(M)\) is the invariant introduced by Toomer and defined as the largest integer \(p\) such that \(E^{p,*}_ \infty\neq 0\) in the Moore spectral sequence: \(\text{Tor}_{H^*(\Omega M;
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The author uses the techniques of rational homotopy theory to prove that for a nilmanifold \(M\), we have: \(\dim M=\text{rank}(\pi_ 1(M))=\text{cat}(M)=e_ 0(M)\). Here \(e_ 0(M)\) is the invariant introduced by Toomer and defined as the largest integer \(p\) such that \(E^{p,*}_ \infty\neq 0\) in the Moore spectral sequence: \(\text{Tor}_{H^*(\Omega M;
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Polynomial Eulerian Characteristic of Nilmanifolds
Functional Analysis and Its ApplicationsThe author gives a comprehensive description of the geometry and algebraic topology of the nilmanifold \(M^n = L^n /\Gamma^n\) with \(L^n\) the Lie group of polynomials \(p(t) = t + x_1t^2 + \cdots + x_nt^{n+1}\) with \(x_i \in \mathbb{R}\) and \(\Gamma^n\) the integer lattice with all \(x_i \in \mathbb{Z}.\) Results include the identification of the ...
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Periodic Points on Nilmanifolds
1981Shub and Sullivan [13] proves that every C1-map f : M → M of a compact smooth manifold has infinitely many periodic points if the Lefschetz numbers L(fk), k = 1,2,..., are unbounded. This is not generally true if f is a continuous map, and even if f is a homeo-morphism (see [11]).
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Spectral Geometry on Nilmanifolds
1997Two Riemannian manifolds are said to be isospectral if the associated Laplace-Beltrami operators have the same spectrum. Riemannian nilmanifolds have provided a rich source of examples of isospectral manifolds, exhibiting a wide variety of different phenomena.
Carolyn S. Gordon, Ruth Gornet
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2013
Nilmanifolds and solvmanifolds appear as “toy-examples” in non-Kahler geometry: indeed, on the one hand, non-tori nilmanifolds admit no Kahler structure, (Benson and Gordon, Topology 27(4):513–518, 1988; Lupton and Oprea, J. Pure Appl. Algebra 91(1–3):193–207, 1994), and, more in general, solvmanifolds admitting a Kahler structure are characterized ...
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Nilmanifolds and solvmanifolds appear as “toy-examples” in non-Kahler geometry: indeed, on the one hand, non-tori nilmanifolds admit no Kahler structure, (Benson and Gordon, Topology 27(4):513–518, 1988; Lupton and Oprea, J. Pure Appl. Algebra 91(1–3):193–207, 1994), and, more in general, solvmanifolds admitting a Kahler structure are characterized ...
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Rational sub-nilmanifolds of a compact nilmanifold
Ergodic Theory and Dynamical Systems, 2006openaire +1 more source