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arXiv · 1511.02904

Spaces of convex n-partitions

Emerson León·Günter M. Ziegler
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Abstract

We construct and study the space C(\R^d,n) of all partitions of \R^d into n non-empty open convex regions (n-partitions). A representation on the upper hemisphere of an n-sphere is used to obtain a metric and thus a topology on this space. We show that the space of partitions into possibly empty regions C(\R^d,\le n) yields a compactification with respect to this metric. We also describe faces and face lattices, combinatorial types, and adjacency graphs for $n$-partitions, and use these concepts to show that C(\R^d,n) is a union of elementary semialgebraic sets.

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Emerson León, Günter M. Ziegler. 2015-11-09. Spaces of convex n-partitions. https://doi.org/10.1007/978-3-662-57413-3

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