Results 111 to 120 of about 402 (139)

Nilmanifolds with Anosov Automorphism

Journal of the London Mathematical Society, 1978
In his survey article [14] S Smalc raised the problem of classifying all Anosov automorphisms of compact manifolds. His conjecture, which is now supported by results of J- Franks [5J and A, Manning [91, is that any Anosov automorphism of a compact manifold is topologically conjugate to a hyperbolic infra-nilmanifold automorphism.
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THERE ARE ONLY FINITELY MANY INFRA-NILMANIFOLDS UNDER EACH NILMANIFOLD

The Quarterly Journal of Mathematics, 1988
Let G be a connected and simply connected nilpotent Lie group and K a maximal compact subgroup of Aut(G). By an (infra-)nilmanifold one means the coset space \(E\setminus G\) where S is a torsion-free discrete uniform lattice of G (G\(\circ K\) resp.). The main result of this work is the following theorem.
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Symplectic structures¶on Heisenberg-type nilmanifolds

manuscripta mathematica, 2000
The authors consider certain nilmanifolds of the form \(T \times\Gamma \setminus N\), where \(T\) is a torus and \(\Gamma\) a discrete co-compact subgroup of a 2-step nilpotent Lie group \(N\). The exterior powers of Lie algebra, \(\wedge^* {\mathfrak n}\), are used to study the existence and classification of symplectic and Kähler structures on \(T ...
Dotti, Isabel, Tirao, Paulo
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Cohomology of Nilmanifolds

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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On Algebraic Anosov Diffeomorphisms on Nilmanifolds

Siberian Mathematical Journal, 2004
Summary: The article is devoted to the algebraic approaches to Anosov diffeomorphisms. All examples of Anosov diffeomorphisms known so far are connected directly or indirectly with compact nilmanifolds. We consider some new necessary conditions for the existence of these diffeomorphisms on nilmanifolds.
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Periodic Points on Nilmanifolds

1981
Shub 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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Polynomial Eulerian Characteristic of Nilmanifolds

Functional Analysis and Its Applications
The 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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Nilmanifolds

2023
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Rational sub-nilmanifolds of a compact nilmanifold

Ergodic Theory and Dynamical Systems, 2006
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Nilmanifolds

1997
Aleksy Tralle, John Oprea
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