On sectioning multiples of the nontrivial line bundle over Grassmannians

Horanská, Ľubomíra

Displaying similar documents to “On sectioning multiples of the nontrivial line bundle over Grassmannians”

Parametrized Borsuk-Ulam problem for projective space bundles

Mahender Singh (2011)

Fundamenta Mathematicae

Similarity:

Let π: E → B be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let π’: E’ → B be a vector bundle such that ℤ₂ acts fiber preserving and freely on E and E’-0, where 0 stands for the zero section of the bundle π’: E’ → B. For a fiber preserving ℤ₂-equivariant map f: E → E’, we estimate the cohomological dimension of the zero set $Z_{f} = x \in E | f (x) = 0$ . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set $A_{f} = x \in E | f (x) = f (T (x))$ of a...

The generic dimension of the first derived system

Robert P. Buemi (1978)

Annales de l'institut Fourier

Similarity:

Any $r$ -dimensional subbundle of the cotangent bundle on an $n$ -dimensional manifold $M$ partitions $M$ into subsets $M_{0}, ..., M_{m}$ ( $m$ being the minimum of $r$ and $C (n - r, 2)$ , the combinations of $n - r$ things taken 2 at a time). $M_{i}$ is the set on which the first derived systems of the subbundle has codimension $i$ . In this paper we prove the following: Theorem. Let $s \geq 2$ and let $Q$ be a generic $C^{s}$ $r$ -dimensional subbundle of the cotangent bundle of an $n$ -dimensional manifold $M$ . The codimension...

Linear liftings of affinors to Weil bundles

Jacek Dębecki (2003)

Colloquium Mathematicae

Similarity:

We give a classification of all linear natural operators transforming affinors on each n-dimensional manifold M into affinors on $T^{A} M$ , where $T^{A}$ is the product preserving bundle functor given by a Weil algebra A, under the condition that n ≥ 2.

Non-existence of some canonical constructions on connections

Włodzimierz M. Mikulski (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

For a vector bundle functor $H : ℳ f \to 𝒱 ℬ$ with the point property we prove that $H$ is product preserving if and only if for any $m$ and $n$ there is an $ℱ ℳ_{m, n}$ -natural operator $D$ transforming connections $Γ$ on $(m, n)$ -dimensional fibered manifolds $p : Y \to M$ into connections $D (Γ)$ on $H p : H Y \to H M$ . For a bundle functor $E : ℱ ℳ_{m, n} \to ℱ ℳ$ with some weak conditions we prove non-existence of $ℱ ℳ_{m, n}$ -natural operators $D$ transforming connections $Γ$ on $(m, n)$ -dimensional fibered manifolds $Y \to M$ into connections $D (Γ)$ on $E Y \to M$ .

Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

The second order transverse bundle $T_{}^{2} M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $𝔻^{2}$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $𝔻^{2}$ -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $𝔻^{2}$ -smooth foliated diffeomorphism between two second order transverse...