Geometry & Topology, Vol. 5 (2001) Paper no. 27, pages 885--893.

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

Michael Eastwood, Paul Norbury

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

AMS subject classification. Primary: 51M04. Secondary: 70G25.

DOI: 10.2140/gt.2001.5.885

E-print: arXiv:math.MG/0109161

Submitted to GT on 26 October 2001. (Revised 10 November 2001.) Paper accepted 26 November 2001. Paper published 26 November 2001.

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Michael Eastwood, Paul Norbury
Pure Mathematics Department
Adelaide University
South Australia 5005
Email: meastwoo@maths.adelaide.edu.au, pnorbury@maths.adelaide.edu.au

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