On counting associative submanifolds and Seiberg-Witten monopoles

DOI10.4310/PAMQ.2019.v15.n4.a4zbMath1436.53035arXiv1712.08383MaRDI QIDQ2308077

Thomas Walpuski, Aleksander Doan

Publication date: 25 March 2020

Published in: Pure and Applied Mathematics Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08383

zbMATH Keywords

Floer homologySeiberg-Witten equationsmonopolesstable pair invariantsDonaldson-Thomas theoryassociative submanifolds\(G^2\)-manifolds

Mathematics Subject Classification ID

Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Applications of global analysis to structures on manifolds (57R57) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Global submanifolds (53C40) Issues of holonomy in differential geometry (53C29) Calibrations and calibrated geometries (53C38) Floer homology (57R58)

Related Items (6)

Counting associatives in compact $G_2$ orbifolds ⋮ Associative submanifolds in Joyce's generalised Kummer constructions ⋮ Castelnuovo's bound and rigidity in almost complex geometry ⋮ On the compactness problem for a family of generalized Seiberg-Witten equations in dimension \(3\) ⋮ Deformation theory of the blown-up Seiberg-Witten equation in dimension three ⋮ Topological \(G_2\) and Spin(7) strings at 1-loop from double complexes

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