G2–instantons over twisted connected sums

Sá Earp, Henrique N¹ ; Walpuski, Thomas²

¹ Unicamp, Universidade Estadual de Campinas, 13083-859 São Paulo, Brazil
² Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA

Geometry & topology, Tome 19 (2015) no. 3, pp. 1263-1285.

Résumé

We introduce a method to construct $G_2$–instantons over compact $G_2$–manifolds arising as the twisted connected sum of a matching pair of building blocks. Our construction is based on gluing $G_2$–instantons obtained from holomorphic vector bundles over the building blocks via the first author’s work. We require natural compatibility and transversality conditions which can be interpreted in terms of certain Lagrangian subspaces of a moduli space of stable bundles on a $K3$ surface.

Détail

DOI : 10.2140/gt.2015.19.1263

Classification : 53C07, 53C25, 53C38
Keywords: gauge theory, $G_2$–manifolds, gluing, holomorphic bundles

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