Lectures and Surveys on G2-Manifolds and Related Topics

This book, one of the first on G2 manifolds in decades, collects introductory lectures and survey articles largely based on talks given at a workshop held at the Fields Institute in August 2017, as part of the major thematic program on geometric analysis. It provides an accessible introduction to various aspects of the geometry of G2 manifolds, including the construction of examples, as well as the intimate relations with calibrated geometry, Yang-Mills gauge theory, and geometric flows. It also features the inclusion of a survey on the new topological and analytic invariants of G2 manifolds that have been recently discovered. The first half of the book, consisting of several introductory lectures, is aimed at experienced graduate students or early career researchers in geometry and topology who wish to familiarize themselves with this burgeoning field. The second half, consisting of numerous survey articles, is intended to be useful to both beginners and experts in the field.

Part I.- Introduction to G2 Geometry (S. Karigiannis).- Constructions of Compact G2-Holonomy Manifolds (A. Kovalev).- Calibrated Submanifolds (J.D. Lotay).- Calibrated Submanifolds in G2 Geometry (K.F. Chan, N.C. Leung).- Geometric Flows of G2 Structures (J.D. Lotay).- Part II.- Distinguishing G2-Manifolds (D. Crowley, S. Goette, J. Nordstrom).- Gravitational Instantons and Degenerations of Ricci-flat Matrics on the K3 Surface (L. Foscolo).- Frolicher-Nijenhuis Bracket on Manifolds with Special Holonomy (K. Kawai, H.V. Le, L. Schwachhofer).- Distinguished G2-Structures on Solvmanifolds (J. Lauret).- On G2-Structures, Special Metrics, and Related Flows (M. Fernandez, A. Fino, A. Raffero).- Laplacian Flow for Closed G2 Structures (Y. Wei).- Flows of Co-Closed Gw-Structers (S. Grigorian).- G2-Instantons on Noncompact G2-Manifolds (J.D. Lotay, G. Oliveira).- Current Progress on G2-Instantons Over Twisted Connected Sums (H. Sa Earp).- Complex and Calibrated Geometry (K. Moore).- Deformations of Calibrated Submanifolds with Boundary (A. Kovalev).