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Lectures and Surveys on G2-Manifolds and Related Topics

  • Spiro Karigiannis
  • Naichung Conan Leung
  • Jason D. Lotay
Book

Part of the Fields Institute Communications book series (FIC, volume 84)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Lectures

    1. Front Matter
      Pages 1-1
    2. Spiro Karigiannis
      Pages 3-50
    3. Jason D. Lotay
      Pages 69-101
    4. Ki Fung Chan, Naichung Conan Leung
      Pages 103-111
  3. Surveys

    1. Front Matter
      Pages 141-141
    2. Diarmuid Crowley, Sebastian Goette, Johannes Nordström
      Pages 143-172
    3. Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer
      Pages 201-215
    4. Marisa Fernández, Anna Fino, Alberto Raffero
      Pages 235-251
    5. Sergey Grigorian
      Pages 271-286
    6. Kim Moore
      Pages 349-364

About this book

Introduction

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.

Keywords

minimal submanifolds special Lagrangians Cayley submanifolds Riemannian holonomy Calabi-Yau manifolds normed division algebras geometric flows torsion forms hyperkahler metrics Dolbeault cohomologies Frolicher-Nijenhuis bracket solitons Einstein metric Ricci soliton Laplacian flow

Editors and affiliations

  • Spiro Karigiannis
    • 1
  • Naichung Conan Leung
    • 2
  • Jason D. Lotay
    • 3
  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Institute of Mathematical SciencesChinese University of Hong KongShatinHong Kong
  3. 3.Mathematical Institute, University of OxfordOxfordUK

Bibliographic information