# homotopy

The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy.

Homotopy is a continuous transformation from one
path in a topological space to
another, or, more generally, of one function to another. Paths connected
by a homotopy are called **homotopic** and are said to be in
the same **homotopy class**. Properties left unchanged by such
homotopies are known as **homotopy invariants**. Homotopy classes
of paths can be composed to form the fundamental
group, or **first homotopy group**. Other maps can be used
to form **higher homotopy groups**.