A proof of Atiyah's conjecture on configurations, of four points in Euclidean three-space

Abstract

From any configuration of finitely many points in Euclidean three-space, Atiyah constructed a determinant and conjectured that it was always non-zero. Atiyah and Sutcliffe (hep-th/0105179) amass a great deal of evidence it its favour. In this article we prove the conjecture for the case of four points.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper27.abs.htm