Geometric structures on G2 and Spin(7)-manifolds

Abstract

This article studies the geometry of moduli spaces of G2-manifolds, associative cycles, coassociative cycles and deformed Donaldson-Thomas bundles. We introduce natural symmetric cubic tensors and differential forms on these moduli spaces. They correspond to Yukawa couplings and correlation functions in M-theory. We expect that the Yukawa coupling characterizes (co-)associative fibrations on these manifolds. We discuss the Fourier transformation along such fibrations and the analog of the Strominger-Yau-Zaslow mirror conjecture for G2-manifolds. We also discuss similar structures and transformations for Spin(7)-manifolds.

Revised and updated version

References in corpus (2)

• The geometry of three-forms in six and seven dimensions
• Moment maps, monodromy and mirror manifolds

Cited by in corpus (6)

• M theory and Singularities of Exceptional Holonomy Manifolds
• Manifolds with parallel differential forms and Kaehler identities for G_2-manifolds
• Moduli spaces of G2 manifolds
• The Topological G2 String
• Intersection theory of coassociative submanifolds in G_(2)-manifolds and Seiberg-Witten invariants
• Cayley 4-form, comass, and triality isomorphisms