Lectures and Surveys on G2-Manifolds and Related Topics

ISBN-13: 9781071605790 / Angielski / Miękka / 2021 / 382 str.

Spiro Karigiannis; Naichung Conan Leung; Jason D. Lotay

Spis treści

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).

Blurb

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.