The ℤ₂-cohomology cup-length of real flag manifolds

Július Korbaš; Juraj Lörinc

Displaying similar documents to “The ℤ₂-cohomology cup-length of real flag manifolds”

On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

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We prove that for any positive integers $n_{1}, n_{2}, ..., n_{k}$ there exists a real flag manifold $F (1, ..., 1, n_{1}, n_{2}, ..., n_{k})$ with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

Pseudosymmetric and Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds

N. Malekzadeh, E. Abedi, U.C. De (2016)

Archivum Mathematicum

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In this paper we classify pseudosymmetric and Ricci-pseudosymmetric $(κ, μ)$ -contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds.

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

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In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: $1_{}$ . if M is a linear manifold, then (M) contains convex functions, $2_{}$ . (·) is invariant under diffeomorphisms, $3_{}$ . each f ∈ (M) is differentiable on a dense $G_{δ}$ -set, is investigated.

Exotic Deformations of Calabi-Yau Manifolds

Paolo de Bartolomeis, Adriano Tomassini (2013)

Annales de l’institut Fourier

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We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) $2 n$ -dimensional symplectic manifolds $(M, κ)$ endowed with a $κ$ -tamed almost complex structure $J$ and with a nowhere vanishing and normalized section $ϵ$ of the bundle $Λ_{J}^{n, 0} (M)$ satisfying the condition ${\bar{\partial}}_{J} ϵ = 0$ . We study the moduli space $𝔐$ of QIS deformations of a given Calabi-Yau manifold, computing its tangent space...

Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

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We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u (t) = U (t, s) u (s) + \int_{s}^{t} U (t, ξ) f (ξ, u (ξ)) d ξ$ when the evolution family ${(U (t, s))}_{t \geq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the...

A note on the cohomology ring of the oriented Grassmann manifolds ${\tilde{G}}_{n, 4}$

Tomáš Rusin (2019)

Archivum Mathematicum

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We use known results on the characteristic rank of the canonical $4$ –plane bundle over the oriented Grassmann manifold ${\tilde{G}}_{n, 4}$ to compute the generators of the $ℤ_{2}$ –cohomology groups $H^{j} ({\tilde{G}}_{n, 4})$ for $n = 8, 9, 10, 11$ . Drawing from the similarities of these examples with the general description of the cohomology rings of ${\tilde{G}}_{n, 3}$ we conjecture some predictions.

On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, Riccardo Ghiloni (2014)

Annales Polonici Mathematici

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Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $= {V_{y}}_{y \in R^{b}}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y \in R^{b} ∖ 0$ (possibly singular over y = 0) and is perfectly parametrized by $R^{b}$ in the sense that $V_{y}$ is birationally nonisomorphic to $V_{z}$ for every $y, z \in R^{b}$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic...

Riemannian regular $σ$ -manifolds

A. A. Ermolitski (1994)

Czechoslovak Mathematical Journal

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Global integral formulas for solving the $\bar{\partial}$ -equation on Stein manifolds

Gennadi M. Henkin, Jürgen Leiterer (1981)

Annales Polonici Mathematici

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$L^{2}$ -cohomology

J. Eichhorn (1986)

Banach Center Publications

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Overconvergent de Rham-Witt cohomology

Christopher Davis, Andreas Langer, Thomas Zink (2011)

Annales scientifiques de l'École Normale Supérieure

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The goal of this work is to construct, for a smooth variety $X$ over a perfect field k of finite characteristic $p > 0$ , an overconvergent de Rham-Witt complex $W^{†} Ω_{X / k}$ as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in $X$ , is a complex of étale sheaves and a differential graded algebra over the ring $W^{†} (𝒪_{X})$ of overconvergent Witt-vectors. If $X$ is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set $S_{C F} (m)$ and that each element of $S_{C F} (m)$ is represented by a manifold with finite holonomy group.

Holonomy groups of flat manifolds with the $R_{\infty}$ property

Rafał Lutowski, Andrzej Szczepański (2013)

Fundamenta Mathematicae

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Let M be a flat manifold. We say that M has the $R_{\infty}$ property if the Reidemeister number R(f) is infinite for every homeomorphism f: M → M. We investigate relations between the holonomy representation ρ of M and the $R_{\infty}$ property. When the holonomy group of M is solvable we show that if ρ has a unique ℝ-irreducible subrepresentation of odd degree then M has the $R_{\infty}$ property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].

On prolongations of projectable connections

Jan Kurek, Włodzimierz M. Mikulski (2011)

Annales Polonici Mathematici

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We extend the concept of r-order connections on fibred manifolds to the one of (r,s,q)-order projectable connections on fibred-fibred manifolds, where r,s,q are arbitrary non-negative integers with s ≥ r ≤ q. Similarly to the fibred manifold case, given a bundle functor F of order r on (m₁,m₂,n₁,n₂)-dimensional fibred-fibred manifolds Y → M, we construct a general connection ℱ(Γ,Λ):FY → J¹FY on FY → M from a projectable general (i.e. (1,1,1)-order) connection $Γ : Y \to J^{1, 1, 1} Y$ on Y → M by means of an...

Non-embeddable $1$ -convex manifolds

Jan Stevens (2014)

Annales de l’institut Fourier

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We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable $1$ -convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type $(1, - 3)$ . To this end we study small resolutions of $c D_{4}$ -singularities.

Homotopy invariance of higher signatures and $3$ -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

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For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable $3$ -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable $3$ -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients...