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Recent Advances in the Theory of Holonomy

Publication ,  Journal Article
Bryant, RL
Published in: Seminaire Bourbaki
October 11, 1999

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.

Duke Scholars

Published In

Seminaire Bourbaki

Publication Date

October 11, 1999

Volume

1998

Issue

99

Start / End Page

351 / 374
 

Citation

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Bryant, R. L. (1999). Recent Advances in the Theory of Holonomy. Seminaire Bourbaki, 1998(99), 351–374.
Bryant, Robert L. “Recent Advances in the Theory of Holonomy.” Seminaire Bourbaki 1998, no. 99 (October 11, 1999): 351–74.
Bryant RL. Recent Advances in the Theory of Holonomy. Seminaire Bourbaki. 1999 Oct 11;1998(99):351–74.
Bryant, Robert L. “Recent Advances in the Theory of Holonomy.” Seminaire Bourbaki, vol. 1998, no. 99, Oct. 1999, pp. 351–74.
Bryant RL. Recent Advances in the Theory of Holonomy. Seminaire Bourbaki. 1999 Oct 11;1998(99):351–374.

Published In

Seminaire Bourbaki

Publication Date

October 11, 1999

Volume

1998

Issue

99

Start / End Page

351 / 374