Manifolds¶
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sage.categories.manifolds.
ComplexManifolds
¶ The category of complex manifolds.
A \(d\)-dimensional complex manifold is a manifold whose underlying vector space is \(\CC^d\) and has a holomorphic atlas.
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sage.categories.manifolds.
Manifolds
¶ The category of manifolds over any topological field.
Let \(k\) be a topological field. A \(d\)-dimensional \(k\)-manifold \(M\) is a second countable Hausdorff space such that the neighborhood of any point \(x \in M\) is homeomorphic to \(k^d\).
EXAMPLES:
sage: from sage.categories.manifolds import Manifolds sage: C = Manifolds(RR); C Category of manifolds over Real Field with 53 bits of precision sage: C.super_categories() [Category of topological spaces]