Affine Hopf fibration
V. Ovsienko, S. Tabachnikov
TL;DR
This paper investigates the existence of affine Hopf fibrations in n-dimensional real affine spaces, providing a classification based on the Hurwitz-Radon function.
Contribution
It characterizes the conditions under which affine Hopf fibrations exist, linking geometric fibrations to algebraic functions like Hurwitz-Radon.
Findings
Existence of affine Hopf fibrations is determined by the Hurwitz-Radon function.
Provides a complete classification for possible (n,p) pairs.
Connects geometric fibrations with algebraic properties of functions.
Abstract
An affine Hopf fibration is a fibration of n-dimensional real affine space by p-dimensional pairwise skew affine subspaces. An example is a fibration of 3-space by pairwise skew lines, the result of the central projection of the classical Hopf fibration of 3-sphere. In this expository article, we describe the solution of the following problem: for which values of n and p does an affine Hopf fibration exist? The answer is given in terms of the Hurwitz-Radon function.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Holomorphic and Operator Theory · Geometric and Algebraic Topology