English

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.

Keywords

Cite

@article{arxiv.2402.05205,
  title  = {Algebraic homotopy classes},
  author = {Juliusz Banecki},
  journal= {arXiv preprint arXiv:2402.05205},
  year   = {2024}
}