MODULI SPACES OF G₂MANIFOLDS

Abstract

This paper is a review of current developments in the study of moduli spaces of G 2 manifolds. G 2 manifolds are seven-dimensional manifolds with the exceptional holonomy group G 2 . Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi–Yau manifolds in seven 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 G 2 manifolds, local deformation theory of G 2 structures and the local geometry of the moduli spaces of G 2 structures.

Locations

• Reviews in Mathematical Physics - View
• arXiv (Cornell University) - View - PDF
• MPG.PuRe (Max Planck Society) - View - PDF
• DataCite API - View