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Lectures and Surveys on G2-Manifolds and Related Topics

  • 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

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

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-1-0716-0577-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 139.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxii
  2. Lectures

    1. Front Matter

      Pages 1-1
    2. Introduction to \(\mathrm {G}_2\) Geometry

      • Spiro Karigiannis
      Pages 3-50
    3. Calibrated Submanifolds

      • Jason D. Lotay
      Pages 69-101
    4. Calibrated Submanifolds in \(G_{2}\) Geometry

      • Ki Fung Chan, Naichung Conan Leung
      Pages 103-111
  3. Surveys

    1. Front Matter

      Pages 141-141
    2. Distinguishing \(G_2\)-Manifolds

      • Diarmuid Crowley, Sebastian Goette, Johannes Nordström
      Pages 143-172
    3. Frölicher–Nijenhuis Bracket on Manifolds with Special Holonomy

      • Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer
      Pages 201-215
    4. On G\(_{\mathbf 2}\)-Structures, Special Metrics and Related Flows

      • Marisa Fernández, Anna Fino, Alberto Raffero
      Pages 235-251
    5. Flows of Co-closed \(G_{2}\)-Structures

      • Sergey Grigorian
      Pages 271-286
    6. Complex and Calibrated Geometry

      • Kim Moore
      Pages 349-364

About this book

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

  • Department of Pure Mathematics, University of Waterloo, Waterloo, Canada

    Spiro Karigiannis

  • Institute of Mathematical Sciences, Chinese University of Hong Kong, Shatin, Hong Kong

    Naichung Conan Leung

  • Mathematical Institute, University of Oxford, Oxford, UK

    Jason D. Lotay

Bibliographic Information

  • Book Title: Lectures and Surveys on G2-Manifolds and Related Topics

  • Editors: Spiro Karigiannis, Naichung Conan Leung, Jason D. Lotay

  • Series Title: Fields Institute Communications

  • DOI: https://doi.org/10.1007/978-1-0716-0577-6

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2020

  • Hardcover ISBN: 978-1-0716-0576-9

  • Softcover ISBN: 978-1-0716-0579-0

  • eBook ISBN: 978-1-0716-0577-6

  • Series ISSN: 1069-5265

  • Series E-ISSN: 2194-1564

  • Edition Number: 1

  • Number of Pages: XXII, 382

  • Number of Illustrations: 79 b/w illustrations, 6 illustrations in colour

  • Topics: Differential Geometry, Algebraic Geometry

Buying options

eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-1-0716-0577-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 139.99
Price excludes VAT (USA)
Hardcover Book USD 139.99
Price excludes VAT (USA)