Complex Polynomial Representation of $π_{n+1}(s^{n})$ and $π_{n+2}(s^{n})$

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dc.creatorTuriel, Francisco-Javier
dc.date2007-02-12
dc.date.accessioned2026-07-07T07:46:20Z
dc.date.available2026-07-07T07:46:20Z
dc.descriptionThe complex affine quadric $Q^{m}=\{z\in {\Bbb C}^{m+1}\mid z_{1}^{2}+...+z_{m+1}^{2}=1\}$ deforms by retraction onto $S^{m}$; this allows us to identify $[Q^{k},Q^{n}]$ and $[S^{k},S^{n}]=π_{k}(S^{n})$. Thus one will say that an element of $π_{k}(S^{n})$ is complex representable if there exists a complex polynomial map from $Q^{k}$ to $Q^{n}$ corresponding to this class. In this Note we show that $π_{n+1}(S^{n})$ and $π_{n+2}(S^{n})$ are complex representable.
dc.description5 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0702324
dc.identifierhttp://arxiv.org/abs/math/0702324
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123796
dc.subjectAlgebraic Topology
dc.titleComplex Polynomial Representation of $π_{n+1}(s^{n})$ and $π_{n+2}(s^{n})$
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