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Lectures and Surveys on G2-Manifolds and Related Topics

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  • © 2020
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Overview

Editors:
  1. Spiro Karigiannis

    1. Department of Pure Mathematics, University of Waterloo, Waterloo, Canada

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  2. Naichung Conan Leung

    1. Institute of Mathematical Sciences, Chinese University of Hong Kong, Shatin, Hong Kong

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    You can also search for this editor in PubMed   Google Scholar

  3. Jason D. Lotay

    1. Mathematical Institute, University of Oxford, Oxford, UK

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  • 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)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxii
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  3. Surveys

    1. Front Matter

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

      • Diarmuid Crowley, Sebastian Goette, Johannes Nordström
      Pages 143-172
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    3. Gravitational Instantons and Degenerations of Ricci-flat Metrics on the K3 Surface

      • Lorenzo Foscolo
      Pages 173-199
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    4. Frölicher–Nijenhuis Bracket on Manifolds with Special Holonomy

      • Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer
      Pages 201-215
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    5. Distinguished \(G_2\)-Structures on Solvmanifolds

      • Jorge Lauret
      Pages 217-233
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    6. On G\(_{\mathbf 2}\)-Structures, Special Metrics and Related Flows

      • Marisa Fernández, Anna Fino, Alberto Raffero
      Pages 235-251
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    7. Laplacian Flow for Closed \(\mathrm{G}_2\) Structures

      • Yong Wei
      Pages 253-269
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    8. Flows of Co-closed \(G_{2}\)-Structures

      • Sergey Grigorian
      Pages 271-286
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    9. \(\mathrm{G}_2\)-Instantons on Noncompact \(\mathrm{G}_2\)-Manifolds: Results and Open Problems

      • Jason D. Lotay, Goncalo Oliveira
      Pages 287-317
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    10. Current Progress on \(\mathrm{{G}}_2\)-Instantons over Twisted Connected Sums

      • Henrique Sá Earp
      Pages 319-348
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    11. Complex and Calibrated Geometry

      • Kim Moore
      Pages 349-364
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    12. Deformations of Calibrated Submanifolds with Boundary

      • Alexei Kovalev
      Pages 365-382
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Keywords

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.


             
 
                              

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: 978-1-0716-0576-9Published: 27 May 2020

  • Softcover ISBN: 978-1-0716-0579-0Published: 28 May 2021

  • eBook ISBN: 978-1-0716-0577-6Published: 26 May 2020

  • 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

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