TY - JOUR

T1 - Construction of G_2-instantons via twisted connected sums

AU - Menet, Grégoire

AU - Nordstrom, Johannes

AU - Sá Earp, Henrique

N1 - Funding Information:
We thank Daniele Faenzi, Marcos Jardim and Thomas Walpuski for many important discussions. In particular, we acknowledge Marcos Jardim for suggesting the Hartshorne-Serre technique to produce bundles parametrised by curves. GM is supported by grant 2014/05733-9, São Paulo Research Foundation (Fapesp), and the Marco Brunella Grant of Burgundy University. HSE is supported by grant 2014/24727-0, São Paulo Research Foundation (Fapesp), and the Brazilian National Council for Scientific and Technological Development (CNPq) Productivity Grant 312390/2014-9. JN is supported by the Simons Foundation under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (grant #488631, Johannes Nordström).

PY - 2021/5/13

Y1 - 2021/5/13

N2 - We propose a method to construct G
2-instantons over a compact twisted connected sum G
2-manifold, applying a gluing result of Sá Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end. In our example, the moduli spaces of the ingredient instantons are non-trivial, and their images in the moduli space over the asymptotic cross-section K3 surface intersect transversely. Such a pair of asymptotically stable holomorphic bundles is obtained using a twisted version of the Hartshorne-Serre construction, which can be adapted to produce other examples. Moreover, their deformation theory and asymptotic behaviour are explicitly understood, results which may be of independent interest.

AB - We propose a method to construct G
2-instantons over a compact twisted connected sum G
2-manifold, applying a gluing result of Sá Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end. In our example, the moduli spaces of the ingredient instantons are non-trivial, and their images in the moduli space over the asymptotic cross-section K3 surface intersect transversely. Such a pair of asymptotically stable holomorphic bundles is obtained using a twisted version of the Hartshorne-Serre construction, which can be adapted to produce other examples. Moreover, their deformation theory and asymptotic behaviour are explicitly understood, results which may be of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=85106344705&partnerID=8YFLogxK

U2 - 10.4310/MRL.2021.v28.n2.a6

DO - 10.4310/MRL.2021.v28.n2.a6

M3 - Article

SN - 1073-2780

VL - 28

SP - 471

EP - 509

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 2

ER -