Relation between spherical designs through a Hopf map

2015/06/28 by Takayuki Okuda, Okuda, Takayuki · 1 citation
Materials Science · Mathematics · #51E30 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Nanocluster Synthesis and Applications #Primary 05B30 #Quasicrystal Structures and Properties #Secondary 43A85 #math.CO #math.MG #msc:05B30 #msc:43A85 #msc:51E30

paper · pdf · doi:10.48550/arxiv.1506.08414

14 pages

arxiv created 2015/06/28 · openalex publication_date 2015/06/28 · arxiv updated 2015/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cohn--Conway--Elkies--Kumar [Experiment. Math. (2007)] described that one can construct a family of designs on S^2n-1 from a design on \mathbbCP^n-1. In this paper, we prove their claim for the case where n=2. That is, we give an algorithm to construct 2t-designs on S³ as products through a Hopf map S³ → S² of a t-design on S² and a 2t-design on S¹.

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