G2–instantons over twisted connected sums

Sá Earp, Henrique N; Walpuski, Thomas

doi:10.2140/gt.2015.19.1263

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$\mathrm{G}_2$–instantons over twisted connected sums

Henrique N Sá Earp and Thomas Walpuski

Geometry & Topology 19 (2015) 1263–1285

DOI: 10.2140/gt.2015.19.1263

Abstract

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 $K 3$ 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

Volume 19, issue 3 (2015)