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 language | English |
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Title of host publication | Lectures and Surveys on G2-manifolds and related topics |
Editors | Spiro Karigiannis, Conan Leung, Jason Lotay |
Publisher | Springer |
Pages | 143-172 |
Number of pages | 30 |
DOIs | |
Publication status | E-pub ahead of print - 27 May 2020 |
Publication series
Name | Fields Institute Communications |
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Volume | 84 |
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