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Recent Advances in the Theory of Holonomy

dc.contributor.author Bryant, Robert
dc.date.accessioned 2016-12-03T19:50:44Z
dc.identifier http://arxiv.org/abs/math/9910059v2
dc.identifier.uri http://hdl.handle.net/10161/13135
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.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
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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