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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

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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 E | f ( x ) = 0 . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set A f = x 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

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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 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

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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

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

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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...