Computational Topology of Equivariant Maps from Spheres to Complements of Arrangements

2004/03/09 by Pavle V. M. Blagojević, Pavle V. M. Blagojevic, Blagojevic, Pavle V. M. +6
Computer Science · Mathematics · #52C35 #55S35 #68U05 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CO #msc:52C35 #msc:55S35 #msc:68U05

paper · pdf · doi:10.48550/arxiv.math/0403161

arxiv created 2004/03/09 · openalex publication_date 2004/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use a well known problem in discrete and computational geometry (partitions of measures by k-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of calculating the obstructions for the existence of equivariant maps. A variety of techniques are introduced and discussed with the emphasis on concrete and explicit calculations. This eventually leads (Theorems 18 and 19) to an almost exhaustive analysis of when such maps do or do not exist in the particular case of interest.

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