Vector Bundles¶
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class
sage.categories.vector_bundles.
VectorBundles
(base_space, base_field, name=None)¶ Bases:
sage.categories.category_types.Category_over_base_ring
The category of vector bundles over any base space and base field.
See also
EXAMPLES:
sage: M = Manifold(2, 'M', structure='top') sage: from sage.categories.vector_bundles import VectorBundles sage: C = VectorBundles(M, RR); C Category of vector bundles over Real Field with 53 bits of precision with base space 2-dimensional topological manifold M sage: C.super_categories() [Category of topological spaces]
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class
Differentiable
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring
The category of differentiable vector bundles.
A differentiable vector bundle is a differentiable manifold with differentiable surjective projection on a differentiable base space.
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class
Smooth
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring
The category of smooth vector bundles.
A smooth vector bundle is a smooth manifold with smooth surjective projection on a smooth base space.
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class
SubcategoryMethods
¶ Bases:
object
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Differentiable
()¶ Return the subcategory of the differentiable objects of
self
.EXAMPLES:
sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).Differentiable() Category of differentiable vector bundles over Real Field with 53 bits of precision with base space 2-dimensional differentiable manifold M
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Smooth
()¶ Return the subcategory of the smooth objects of
self
.EXAMPLES:
sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).Smooth() Category of smooth vector bundles over Real Field with 53 bits of precision with base space 2-dimensional differentiable manifold M
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base_space
()¶ Return the base space of this category.
EXAMPLES:
sage: M = Manifold(2, 'M', structure='top') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).base_space() 2-dimensional topological manifold M
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super_categories
()¶ EXAMPLES:
sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).super_categories() [Category of topological spaces]
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class