Harmonic maps between three-spheres
Piotr Bizo\'n
TL;DR
This paper demonstrates the existence of two countable families of harmonic maps within specific homotopy classes from the three-sphere to itself, highlighting their structure and properties.
Contribution
It identifies and characterizes harmonic maps in homotopy classes of degree zero and one between three-spheres, expanding understanding of harmonic map classifications.
Findings
Two countable families of harmonic maps are contained in the homotopy classes of degree zero and one.
The paper establishes the existence of these harmonic representatives.
It provides a framework for understanding harmonic maps between three-spheres.
Abstract
It is shown that smooth maps contain two countable families of harmonic representatives in the homotopy classes of degree zero and one.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology