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Maclean, R., Beveridge, C., Longcope, D.W., Brown, D.S. and Priest, E.R., 2005, A topological analysis of the magnetic breakout model for an eruptive solar flare, Proc. Roy. Soc., 461, 2099-2120. Sponsorship: PPARC/STFCThe magnetic breakout model gives an elegant explanation for the onset of an eruptive solar flare, involving magnetic reconnection at a coronal null point which leads to initially enclosed flux 'breaking out' to large distances. In this paper we take a topological approach to the study of the conditions required for this breakout phenomenon to occur. The evolution of a simple delta sunspot model, up to the point of breakout, is analysed through several sequences of potential and linear force-free quasi-static equilibria. We show that any new class of field lines, such as those connecting to large distances, must be created through a global topological bifurcation, and derive rules to predict the topological reconfiguration due to various types of bifurcation.Peer reviewe