A new proof of Atiyah’s conjecture on configurations of four points

What is it about?

There is a nice geometric problem due to Sir Michael Atiyah related to configurations of points in space. Given a configuration of n distinct points in space, Atiyah constructs, in a natural geometric way, n complex polynomials of degree at most n - 1. He then conjectured that these polynomials are always linearly independent over C. If true, this would provide an explicit solution to another problem, called the Berry--Robbins problem. The linear independence conjecture was proved for n = 2, 3 by Atiyah and for n = 4 by Eastwood and Norbury. I provide an alternative, hopefully easier proof for the case n = 4.

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Why is it important?

I hope this will lead to some future results on the Atiyah problem on configurations for n > 4 points.