Maps of manifolds

thumb|The two dashed Path (topology)|paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one topological space to another are called homotopic (from and ) if one can be "continuously deformed" into the other, such a deformation being called a homotopy ( ; ) between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.

In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.

differentiable function whose derivative is everywhere injective

construct allowing differentiation of tangent vector fields of manifolds

differentiable map whose differential is everywhere surjective

math/physics concept

generalization of affine connections

Ehresmann connection on a principal bundle that is compatible with the group action

concept in toplogy