Construction of G_2-instantons via twisted connected sums

Grégoire Menet, Johannes Nordstrom, Henrique Sá Earp

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5 Citations (SciVal)

Abstract

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.

Original languageEnglish
Pages (from-to)471-509
Number of pages39
JournalMathematical Research Letters
Volume28
Issue number2
DOIs
Publication statusPublished - 13 May 2021

Bibliographical note

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).

ASJC Scopus subject areas

  • General Mathematics

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