Remarks on the Relations between Non Abelian de Rham Theories with respect to G and ΩG

概要

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Let G be GL (n,c) and ΩG the based loop group over G. Then the (stable) first and second non abelian de Rham sets with respect to G and ΩG are related by the diagram … Here, ΩMe is the space of zero homotopic loops over M, g is the Lie algebra of G, Ωg is the loop algebra over g, and M¹ and M¹Ωg are the sheaves of germs of g- and Ωg-valued integrable forms on M, a smooth Hilbert manifold. The maps ρ*i, B₀ and B₁ are denned by using Grassmanhian model of loop qroups (B is defined with some additional assumptions at this stage). Geometric characterization of the map from M into ΩG, the basic central extension of ΩG, together with its quantization condition and relations of several characteristic classes of non abelian de Rham sets, including string classes, and the above maps are also given.
信州大学理学部の論文
1989-03-30