Title: Introduction to G2 geometry
Spiro Karigiannis
Abstract: These notes give an informal and leisurely introduction to G2 geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in 7 dimensions that is the pointwise model for G2 geometry, using the octonions. The basics of G2-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general G2-structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free G2 manifolds are considered, and we stress the similarities and differences with Ka ̈hler and Calabi-Yau manifolds. The notes end with a brief survey of three important theorems about compact torsion-free G2 manifolds.