# Manifolds¶

This is the Sage implementation of manifolds resulting from the SageManifolds project. This section describes only the “manifold” part of SageManifolds; the pure algebraic part is described in the section Tensors on free modules of finite rank.

More documentation (in particular example worksheets) can be found here.

- Topological Manifolds
- Topological Manifolds
- Subsets of Topological Manifolds
- Manifold Structures
- Points of Topological Manifolds
- Coordinate Charts
- Scalar Fields
- Continuous Maps
- Submanifolds of topological manifolds
- Topological Vector Bundles
- Families of Manifold Objects
- Topological Closures of Manifold Subsets
- Manifold Subsets Defined as Pullbacks of Subsets under Continuous Maps

- Differentiable Manifolds
- Differentiable Manifolds
- Coordinate Charts on Differentiable Manifolds
- The Real Line and Open Intervals
- Scalar Fields
- Differentiable Maps and Curves
- Tangent Spaces
- Vector Fields
- Tensor Fields
- Differential Forms
- Mixed Differential Forms
- De Rham Cohomology
- Alternating Multivector Fields
- Affine Connections
- Submanifolds of differentiable manifolds
- Differentiable Vector Bundles

- Pseudo-Riemannian Manifolds
- Utilities for Calculus
- Manifolds Catalog