Homotopy group

In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The many different ways to (continuously) map an n-dimensional sphere into a given space are collected into equivalence classes, called homotopy classes. Two mappings are homotopic if one can be continuously deformed into the other. These homotopy classes form a group, called the n-th homotopy group of the given space. Topological spaces with differing homotopy groups are never equivalent (homeomorphic), but the converse is not true. The first homotopy group is also called the fundamental group.

Related Topics:
Mathematics - Algebraic topology - Topological space - Sphere - Equivalence class - Homotopy class - Group - Homeomorphic - Fundamental group

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