Convex equipartitions via equivariant obstruction theory

Convex equipartitions via equivariant obstruction theory

Pavle V. M. Blagojević, Günter M. Ziegler – 2012

Focus Area 3: Topological connectivity and diameter of Discrete Structures
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

Title

Convex equipartitions via equivariant obstruction theory