$\pi_n(S^n)=[S^n,S^n]=$ cobordism \pi_n(S^n)=[S^n,S^n]=\lbrace$cobordism classes of framed submanifolds of dimension zero (0-submanifolds$\rbrace$ by the Pontrjagin-Thom construction)construction. These are collections of points (with sign), and sign) which add up to give the degree of the mapmaps, so this set is isomorphic to precisely $\mathbb{Z}$.
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$\pi_n(S^n)=[S^n,S^n]=$ equivalence cobordism classes of framed submanifolds of dimension zero (by the Pontrjagin-Thom construction). These are points (with sign), and add up to give the degree of the map, so is isomorphic to $\mathbb{Z}$. |
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Post Made Community Wiki by S. Carnahan♦
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