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We use a well known problem in discrete and computational geometry(partitions of measures by $k$-fans) as a motivation and as a point ofdeparture to illustrate many aspects, both theoretical and computational, ofthe problem of calculating the obstructions for the existence of equivariantmaps. A variety of techniques are introduced and discussed with the emphasis onconcrete 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 theparticular case of interest.

Computational topology of equivariant maps from spheres to complements of arrangements