Found Phys https://doi.org/10.1007/s10701-018-0139-2 The Relativistic Geometry and Dynamics of Electrons M. F. Atiyah 1 · J. Malkoun 2 Received: 8 January 2018 / Accepted: 16 January 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Atiyah and Sutcliffe (Proc R Soc Lond Ser A 458:1089–1115, 2002) made a number of conjectures about configurations of N distinct points in hyperbolic 3-space, arising from ideas of Berry and Robbins (Proc R Soc Lond Ser A 453:1771–1790, 1997). In this paper we prove all these conjectures, purely geometrically, but we also provide a physical interpretation in terms of Electrons. Keywords Atiyah–Sutcliffe conjectures · Geometry · Berry–Robbins problem · Dynamics · Electrons 1 Introduction Berry and Robbins [8] in 1997 were looking for a classical proof of the spin-statistics theorem and this led them to a purely geometric conjecture about the configuration space C ( N , R 3 ) of N distinct ordered points in 3-space. A non-unitary form of their conjecture was that there should be a continuous map f N : C ( N , R 3 ) → GL ( N , C)/(C ∗ ) N (1.1) B J. Malkoun joseph.malkoun@ndu.edu.lb M. F. Atiyah m.atiyah@ed.ac.uk 1 School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Edinburgh EH9 3FD, UK 2 Department of Mathematics and Statistics, Notre Dame University-Louaize, P.O.Box: 72, Zouk Mikael, Zouk Mosbeh, Lebanon 123