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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$\mathrm{G}_2$–instantons over twisted connected sums

Henrique N Sá Earp and Thomas Walpuski

Geometry & Topology 19 (2015) 1263–1285
Abstract

We introduce a method to construct G2–instantons over compact G2–manifolds arising as the twisted connected sum of a matching pair of building blocks. Our construction is based on gluing G2–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.

Keywords
gauge theory, $G_2$–manifolds, gluing, holomorphic bundles
Mathematical Subject Classification 2010
Primary: 53C07, 53C25, 53C38
References
Publication
Received: 29 October 2013
Revised: 19 May 2014
Accepted: 27 June 2014
Published: 21 May 2015
Proposed: Ronald Stern
Seconded: Richard Thomas, Yasha Eliashberg
Authors
Henrique N Sá Earp
Unicamp
Universidade Estadual de Campinas
13083-859 São Paulo
Brazil
Thomas Walpuski
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307
USA