Convex Equipartitions via Equivariant Obstruction Theory

Details Convex Equipartitions via Equivariant Obstruction Theory Convex Equipartitions via Equivariant Obstruction Theory

2012-02-24

arxiv.org/abs/1202.5504v2

Mathematics

Algebraic Topology

Revised and improved version with new notation, additional references, etc. 17 pages, 7 figures

Scientific paper

We describe a regular cell complex model for the configuration space F(\R^d,n). Based on this, we use equivariant obstruction theory in order to prove the prime power case of the conjecture by Nandakumar and Ramana Rao that every polygon can be partitioned into n convex parts of equal area and perimeter. For a generalization of the conjecture we get a complete answer: It holds IF AND ONLY IF n is a prime power.

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