In algebraic topology, a homotopy group is an important algebraic invariant that captures the topological structure of a space. The most common homotopy groups are the fundamental group and higher homotopy groups. 1. **Fundamental Group (\(\pi_1\))**: The fundamental group is the first homotopy group and provides a measure of the "loop structure" of a space.
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The th homotopy group consists of based homotopy classes of maps . It is a group for and an abelian group for .