Spheres over fields, their entire rational maps and applications

Abstract

The paper summarizes some results on algebraic geometry presence in the homotopy theory. For the homotopy group πm(Sn), denote by πalgm(Sn) its subset of homotopy classes represented by ℝ-entire rational maps Sm→Sn of spheres. The main result of this paper concerns to the study of πn+kalg(Sn) for k=0,...,7.

Keywords

• algebraic set
• c∞-topology
• coordinate ring
• homotopy group
• polynomial (entire rational) map
• sphere
• suspension
• zariski topology