nLab
winding number

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

A continuous function between two topological spaces that are each weakly homotopy equivalent to the circle is, up to homotopy, defined by how much it “winds” one circle around the other. This is its winding number, an integer. Equivalently this is the element in the fundamental group of the codomain which is represented by the map.

A special case of the degree of a continuous function.

Last revised on July 1, 2017 at 11:49:54. See the history of this page for a list of all contributions to it.