The exceptional holonomy groups and calibrated geometry
| dc.creator | Joyce, Dominic | |
| dc.date | 2004-06-01 | |
| dc.date.accessioned | 2026-07-07T06:32:37Z | |
| dc.date.available | 2026-07-07T06:32:37Z | |
| dc.description | The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat. This is a survey paper on exceptional holonomy, in two parts. Part I introduces the exceptional holonomy groups, and explains constructions for compact 7- and 8-manifolds with holonomy G2 and Spin(7). The simplest such constructions work by using techniques from complex geometry and Calabi-Yau analysis to resolve the singularities of a torus orbifold T^7/G or T^8/G, for G a finite group preserving a flat G2 or Spin(7)-structure on T^7 or T^8. There are also more complicated constructions which begin with a Calabi-Yau manifold or orbifold. Part II discusses the calibrated submanifolds of G2 and Spin(7)-manifolds: associative 3-folds and coassociative 4-folds for G2, and Cayley 4-folds for Spin(7). We explain the general theory, following Harvey and Lawson, and the known examples. Finally we describe the deformation theory of compact calibrated submanifolds, following McLean. | |
| dc.description | 32 pages. Lectures given at a conference in Gokova, Turkey, May 2004 | |
| dc.identifier | https://arxiv.org/abs/math/0406011 | |
| dc.identifier | http://arxiv.org/abs/math/0406011 | |
| dc.identifier | pages 110-139 in S. Akbulut, T. Onder and R.J. Stern, editors, 'Proceedings of the Gokova Geometry-Topology Conference 2005', International Press, Somerville, MA, 2006. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98953 | |
| dc.subject | Differential Geometry | |
| dc.title | The exceptional holonomy groups and calibrated geometry | |
| dc.type | text |