Manifolds

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.

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]