# topics in manifold theory

A is a space that is locally like $\mathbb{R}^{n}$, however lacking a preferred system of coordinates. Furthermore, a manifold can have global topological properties, such as non-contractible loops (http://planetmath.org/Curve), that distinguish it from the topologically trivial $\mathbb{R}^{n}$.

By imposing different restrictions on the transition functions of a manifold, one obtain different types of manifolds:

Special types of manifolds

On manifolds, one can introduce more . Some examples are:

## Examples

• space-time manifold in general relativity

• phase space in mechanics