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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
79
6 farbige Abbildungen, 79 s/w Abbildungen
XXII, 382 p. 85 illus., 6 illus. in color.
Dateigröße
ISBN-13
978-1-0716-0577-6 (9781071605776)
DOI
10.1007/978-1-0716-0577-6
Schweitzer Klassifikation
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).
