Moduli spaces of G2 manifolds

Abstract

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.

31 pages, 2 figures

References in corpus (7)

• M theory and Singularities of Exceptional Holonomy Manifolds
• Hodge Theory for G2-manifolds: Intermediate Jacobians and Abel-Jacobi maps
• Local geometry of the G2 moduli space
• Deformations of asymptotically cylindrical G_2 manifolds
• Desingularization of G_2 manifolds with isolated conical singularities
• Betti numbers of a class of barely G2 manifolds
• Geometric construction of the r-map: from affine special real to special Kähler manifolds

Cited by in corpus (18)

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• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Effective action from M-theory on twisted connected sum $G_2$-manifolds
• Superconformal algebras for twisted connected sums and $G_2$ mirror symmetry
• Compact G2 holonomy spaces from SU(3) structures
• Marginal deformations of heterotic $G_2$ sigma models
• Modified Laplacian coflow of $G_2$-structures on manifolds with symmetry
• Components of Eleven-dimensional Supergravity with Four Off-shell Supersymmetries
• G2-structures for N=1 supersymmetric AdS4 solutions of M-theory
• G2-structure deformations and warped products
• G-structures and Superstrings from the Worldsheet
• Conformal transformations of the pseudo-Riemannian metric of a homogeneous pair
• The alpha'-Expansion of Calabi-Yau Compactifications
• The Space of Closed $G_2$-Structures. I. Connections
• Geometry and periods of $G_2$-moduli spaces