A Setting for A Theorem of Bott
نویسندگان
چکیده
منابع مشابه
The Bott Periodicity Theorem
The Bott periodicity theorem is of fundamental importance in many areas of mathematics, from algebraic topology to functional analysis. It appears unexpectedly in different guises and I would like to explain some of these as well as the influence it has had on the development of different fields. I will concentrate on two roles that periodicity plays. First, periodicity allows one to deloop cla...
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A new proof of the Bott periodicity theorem
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The aim of this note is to provide a quick proof of the Borel-Weil-Bott theorem, which describes the cohomology of line bundles on flag varieties. Let G denote a reductive algebraic group over the field C of complex numbers. We let B denote a Borel subgroup of G, and X = G/B be quotient of G by B, acting by right multiplication. The quotient X is a compact complex manifold. The anticanonical bu...
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Throughout this paper, C denotes a smooth projective curve of genus at least one, G denotes a reductive linear algebraic group over C, and ξ0 is a C ∞ principal G-bundle over C. The space of all (0, 1)-connections on ξ0 is an affine space A = A(ξ0) associated to the infinite dimensional complex vector space H0,1(C; ad ξ0). Following Shatz [6] for the case G = GL(n), Atiyah and Bott [1] defined ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1970
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.65.1.8