Abstract
We study topological and combinatorial structures that arise in the problem of finding α-partitions of m spherical measures by k-fans. An elegant construction of I. Bárány and J. Matoušek, [[3]], [[4]], shows that this problem can be reduced to the question whether there exists a G-equivariant map f: V 2(ℝ3) → VP \ ∩AP where G is a subgroup of a dihedral group \( \mathbb{D}_{2n} \) while the target space VP\∩AP is the complement of a G-invariant, linear subspace arrangement AP. We demonstrate that in many cases the relevant topological obstructions for the existence of these equivariant maps can be computed by a variety of geometric, combinatorial and algebraic ideas.
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Vrećica, S.T., Živaljević, R.T. (2003). Arrangements, Equivariant Maps and Partitions of Measures by k-Fans. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_40
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DOI: https://doi.org/10.1007/978-3-642-55566-4_40
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