Construction of G(2)-instantons via twisted connected sums

Autor(es)

Menet, Gregoire ^[1] ; Nordstrom, Johannes ^[2] ; Earp, Henrique N. Sa ^[3]

Afiliação do(s) autor(es)

^[1] Univ Grenoble Alpes, Inst Fourier, 100 Rue Math, F-38610 Gieres - France

^[2] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon - England

^[3] Univ Campinas UNICAMP, Inst Math Stat & Sci Comp, R Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICAL RESEARCH LETTERS; v. 28, n. 2, p. 471-509, 2021.
• Citações Web of Science: 0

Resumo

We propose a method to construct G(2)-instantons over a compact twisted connected sum G(2)-manifold, applying a gluing result of Sa 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. (AU)

• Processo FAPESP: 14/05733-9 - Geometria de variedades simpléticas irredutíveis
• Beneficiário: Grégoire Menet
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 14/24727-0 - G2-instantons sobre somas conexas torcidas
• Beneficiário: Henrique Nogueira de Sá Earp
• Modalidade de apoio: Auxílio à Pesquisa - Regular