Distinguishing G2-manifolds

Diarmuid Crowley, Sebastian Goette, Johannes Nordström

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)

Abstract

In this survey, we describe invariants that can be used to distinguish connected components of the moduli space of holonomy G2 metrics on a closed 7-manifold, or to distinguish -manifolds that are homeomorphic but not diffeomorphic. We also describe the twisted connected sum and extra-twisted connected sum constructions used to realise G2-manifolds for which the above invariants differ.

Original languageEnglish
Title of host publicationLectures and Surveys on G2-manifolds and related topics
EditorsSpiro Karigiannis, Conan Leung, Jason Lotay
PublisherSpringer
Pages143-172
Number of pages30
DOIs
Publication statusE-pub ahead of print - 27 May 2020

Publication series

NameFields Institute Communications
Volume84
ISSN (Print)1069-5265
ISSN (Electronic)2194-1564

Funding

We thank Jean-Michel Bismut, Uli Bunke, Xianzhe Dai, Matthias Lesch for inspiring discussions on adiabatic limits and variational formulas for ?-invariants on manifolds with boundary. We thank Alessio Corti, Jesus Martinez Garcia, David Morrison, Emanuel Scheidegger and Katrin Wendland for helpful information about K 3-surfaces and Fano threefolds. We also thank Mark Haskins and Arkadi Schelling for talking with us about G2-manifolds and G2-bordism. We are particularly indebted to Don Zagier for his formula for Fk,? (s) in Sect. 4.3. SG and JN would like to thank the Simons foundation for its support of their research under the Simons Collaboration on ?Special Holonomy in Geometry, Analysis and Physics? (grants #488617, Sebastian Goette, and #488631, Johannes Nordstr?m).

Keywords

  • 58J28
  • Primary: 57R20
  • Secondary: 53C29

ASJC Scopus subject areas

  • General Mathematics

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