New York Journal of Mathematics
Volume 20 (2014) 293-323


Joel Fine, Kirill Krasnov, and Dmitri Panov

A gauge theoretic approach to Einstein 4-manifolds

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Published: April 7, 2014
Keywords: Einstein manifolds, 4-manifolds, gauge theory
Subject: 53C25, 53C07, 53D35, 58E30

This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.


JF was supported by an Action de Recherche Concertée and by an Interuniversity Action Poles grant.
KK was supported by ERC Starting Grant 277570-DIGT
DP is a Royal Society Research Fellow

Author information

Joel Fine:
Département de mathématique, Université libre de Bruxelles, Bruxelles 1050, Belgium

Kirill Krasnov:
School of Mathematical Sciences, University Park, Nottingham, NG7 2RD, United Kingdom

Dmitri Panov:
Department of Mathematics, King's College, Strand, London WC2R 2LS, United Kingdom