Algebraic homotopy classes
Algebraic Geometry
2024-06-18 v1
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.
Cite
@article{arxiv.2402.05205,
title = {Algebraic homotopy classes},
author = {Juliusz Banecki},
journal= {arXiv preprint arXiv:2402.05205},
year = {2024}
}