On the combinatorics of Murai spheres and its applications
Abstract
We classify the combinatorial types of Murai spheres in dimensions 1 and 2, thereby showing that the corresponding convex simple polytopes have Delzant realizations. Then we describe all chordal Murai spheres Bierc(M) with c∈ Nm and m≤ 2. Finally, we find all possible values for the Buchstaber and chromatic numbers of arbitrary Murai spheres.
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