Recent Advances in the Theory of Holonomy

Details Recent Advances in the Theory of Holonomy Recent Advances in the Theory of Holonomy

1999-10-11

arxiv.org/abs/math/9910059v2

Seminaire Bourbaki, Volume 1998/99, Asterisque 266 (2000), 351-374

Mathematics

Differential Geometry

24 pages, plain tex with amssym.tex and amssym.def. To appear in Asterisque. This is the text of a report to the Seminaire Bou

Scientific paper

This article is a report on the status of the problem of classifying the irriducibly acting subgroups of GL(n,R) that can appear as the holonomy of a torsion-free affine connection. In particular, it contains an account of the completion of the classification of these groups by Chi, Merkulov, and Schwachhofer as well as of the exterior differential systems analysis that shows that all of these groups do, in fact, occur. Some discussion of the results of Joyce on the existence of compact examples with holonomy G_2 or Spin(7) is also included.

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