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Publications [#243383] of Robert Bryant


Papers Published

  1. Bryant, R, Recent advances in the theory of holonomy, Astérisque, vol. 266 no. 5 (December, 2000), pp. 351-374, Centre National de la Recherche Scientifique (Exposé No. 861.) [MR2001h:53067], [math.DG/9910059], [html]
    (last updated on 2019/08/19)

    Author's Comments:
    This is the text of a lecture that I gave June 1999 in the Bourbaki Seminar. As the title suggests, it surveys recent progress in the description of the possible holonomy of a torsion-free connection with irreducibly acting holonomy, both for local structures and global structures.

    After its introduction by Élie Cartan, the notion of holonomy has become increasingly important in Riemannian and affine geometry. Beginning with the fundamental work of Marcel Berger, the classification of possible holonomy groups of torsion free connections, either Riemannian or affine, has continued to be developed, with major breakthroughs in the last ten years. I will report on the local classification in the affine case, Joyce's fundamental work on compact manifolds with exceptional holonomies and their associated geometries, and some new work on the classification of holonomies of connections with restricted torsion, which has recently become of interest in string theory.
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