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arXiv · 2402.05205

Algebraic homotopy classes

Juliusz Banecki
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Abstract

We prove several positive results regarding representation of homotopy classes of spheres and algebraic groups by regular mappings. Most importantly we show that every mapping from a sphere to an orthogonal or a unitary group is homotopic to a regular one. Furthermore we prove that algebraic homotopy classes of spheres form a subgroup of the homotopy group, and that a similar result holds also for cohomotopy groups of arbitrary varieties.

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Juliusz Banecki. 2024-02-07. Algebraic homotopy classes. https://doi.org/10.1016/j.matpur.2024.05.011

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