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The space of hyperkähler metrics on a 4-manifold with boundary

par Fine, Joel ;Lotay, Jason Dean;Singer, Michael
Référence Forum of Mathematics, Sigma, 5
Publication Publié, 2017

Article révisé par les pairs

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Résumé :

Let be a compact 4-manifold with boundary. We study the space of hyperkähler triples on , modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent space in terms of triples of closed anti-self-dual 2-forms. We also explore the corresponding boundary value problem: a hyperkähler triple restricts to a closed framing of the bundle of 2-forms on the boundary; we identify the infinitesimal deformations of this closed framing that can be filled in to hyperkähler deformations of the original triple. Finally we study explicit examples coming from gravitational instantons with isometric actions of .