Results 111 to 120 of about 317 (142)

THE CATEGORY OF NILMANIFOLDS

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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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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A Decomposition Theorem for Complex Nilmanifolds

Canadian Mathematical Bulletin, 1987
AbstractA complex nilmanifold X is isomorphic to a product X ⋍ ℂp x N/┌, where N is a simply connected nilpotent complex Lie group and ┌ is a discrete subgroup of N not contained in a proper connected complex subgroup of N. The pair (N, ┌) is uniquely determined up to holomorphic group isomorphisms.
Loeb, Jean-Jacques, Oeljeklaus, Karl, Richthofer, Wolfgang   +2 more
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Submersions on nilmanifolds and their geodesics

Publicationes Mathematicae Debrecen, 2003
Summary: We describe the geodesics of two-step nilpotent Lie groups \(N\) with respect to left invariant Riemannian metrics \(\langle. ,.\rangle\) using the Riemannian submersion structure of the fiber bundle \(\pi :N\rightarrow N/\mathcal Z\), where \(\mathcal Z\) denotes the center of \(N\).
Homolya, Szilvia, Nagy, Péter T.
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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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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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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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Spectral Geometry on Nilmanifolds

1997
Two 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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Möbius disjointness for skew products on a circle and a nilmanifold

Discrete and Continuous Dynamical Systems, 2021
Wen Huang
exaly