Glossary of differential geometry and topology

This is a glossary of terms specific to differential geometry and differential topology. The following three glossaries are closely related:

See also:

Words in italics denote a self-reference to this glossary.

Atlas

Bundle, see fiber bundle.

Chart

Cobordism

Codimension. The codimension of a submanifold is the dimension of the ambient space minus the dimension of the submanifold.

Connected sum

Connection

Cotangent bundle, the vector bundle of cotangent spaces on a manifold.

Cotangent space

Diffeomorphism. Given two differentiable manifolds M and N, a bijective map ${\displaystyle f}$ from M to N is called a diffeomorphism if both ${\displaystyle f:M\to N}$ and its inverse ${\displaystyle f^{-1}:N\to M}$ are smooth functions.

...
Wikipedia