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

Michael Eastwood and Paul Norbury

Geometry & Topology 5 (2001) 885–893

arXiv: math.MG/0109161

Abstract

From any configuration of finitely many points in Euclidean three-space, Atiyah constructed a determinant and conjectured that it was always non-zero. In this article we prove the conjecture for the case of four points.

Keywords
Atiyah's conjecture, configuration space
Mathematical Subject Classification 2000
Primary: 51M04
Secondary: 70G25
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Publication
Received: 26 October 2001
Revised: 10 November 2001
Accepted: 26 November 2001
Published: 26 November 2001
Proposed: Walter Neumann
Seconded: Ralph Cohen, Steven Ferry
Authors
Michael Eastwood
Pure Mathematics Department
Adelaide University
South Australia 5005
Australia
Paul Norbury
Pure Mathematics Department
Adelaide University
South Australia 5005
Australia