Recent Advances in the Theory of Holonomy

dc.contributor.author

Bryant, Robert L

dc.date.accessioned

2016-12-03T19:50:44Z

dc.description.abstract

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.

dc.format.extent

24 pages, plain tex with amssym.tex and amssym.def.

dc.identifier

http://arxiv.org/abs/math/9910059v2

dc.identifier.uri

https://hdl.handle.net/10161/13135

dc.relation.ispartof

Seminaire Bourbaki

dc.subject

math.DG

dc.subject

math.DG

dc.subject

53C10 (Primary), 53B05 (Secondary)

dc.title

Recent Advances in the Theory of Holonomy

dc.type

Journal article

duke.contributor.orcid

Bryant, Robert L|0000-0002-4890-2471

pubs.author-url

http://arxiv.org/abs/math/9910059v2

pubs.begin-page

351

pubs.end-page

374

pubs.issue

99

pubs.notes

To appear in Asterisque. This is the text of a report to the Seminaire Bourbaki in June 1999. Amended to include the new exotic symplectic example of Spin(6,H) in GL(32,R)

pubs.organisational-group

Duke

pubs.organisational-group

Mathematics

pubs.organisational-group

Trinity College of Arts & Sciences

pubs.volume

1998

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