Category:Homotopy Groups
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This category contains results about Homotopy Groups.
Definitions specific to this category can be found in Definitions/Homotopy Groups.
Let $X$ be a topological space.
Let $x_0 \in X$.
Let $n \in \Z_{>0}$ be a (strictly) positive integer.
Let $\mathbb S^n \subseteq \R^{n + 1}$ be the $n$-sphere.
Let $\mathbf a \in \mathbb S^n$.
Let $\map {\pi_n} {X, x_0}$ be the set of homotopy classes relative to $\mathbf a$ of continuous mappings $f: \mathbb S^n \to X$ such that $\map f {\mathbf a} = x_0$.
Then $\map {\pi_n} {X, x_0}$ is the $n$th homotopy group of $X$.
The group operation of $\map {\pi_n} {X, x_0}$ is the concatenation operation.
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