Lectures and Surveys on G2-Manifolds and Related Topics

This book, one of the first on G 2 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 G 2 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 G 2 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.

Is among the first new books on G2 manifolds in decades Features introductory lectures on several aspects of G2 geometry by recognized experts in the field Serves as an accessible entry point for early career researchers looking to work in the field Contains survey articles on numerous recent developments in G2 geometry and related topics

Texte du rabat

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.

Contenu
Part I.- Introduction to G 2 Geometry (S. Karigiannis).- Constructions of Compact G 2 -Holonomy Manifolds (A. Kovalev).- Calibrated Submanifolds (J.D. Lotay).- Calibrated Submanifolds in G 2 Geometry (K.F. Chan, N.C. Leung).- Geometric Flows of G 2 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 G 2 -Structures on Solvmanifolds (J. Lauret).- On G 2 -Structures, Special Metrics, and Related Flows (M. Fernandez, A. Fino, A. Raffero).- Laplacian Flow for Closed G 2 Structures (Y. Wei).- Flows of Co-Closed Gw-Structers (S. Grigorian).- G 2 -Instantons on Noncompact G2-Manifolds (J.D. Lotay, G. Oliveira).- Current Progress on G 2 -InstantonsOver Twisted Connected Sums (H. Sa Earp).- Complex and Calibrated Geometry (K. Moore).- Deformations of Calibrated Submanifolds with Boundary (A. Kovalev).