101,046 research outputs found

    Homology and K-theory of the Bianchi groups

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    We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group homology and equivariant KK-homology. By the Baum/Connes conjecture, which holds for the Bianchi groups, we obtain the KK-theory of their reduced C∗C^*-algebras in terms of isomorphic images of the computed KK-homology. We further find an application to Chen/Ruan orbifold cohomology. % {\it To cite this article: Alexander D. Rahm, C. R. Acad. Sci. Paris, Ser. I +++ (2011).

    A Review of the Genus \u3ci\u3eGryllus\u3c/i\u3e (Orthoptera: Gryllidae), With a New Species From Korea

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    Gryllus is the most widely distributed genus of the Tribe Gryllini, and may be the largest; it includes 69 described species occupying most of the New World, Africa, and Europe, and much of Asia. A new species from Korea significantly extends the known range of the genus

    Loop groups in Yang-Mills theory

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    We consider the Yang-Mills equations with a matrix gauge group GG on the de Sitter dS4_4, anti-de Sitter AdS4_4 and Minkowski R3,1R^{3,1} spaces. On all these spaces one can introduce a doubly warped metric in the form ds2=−du2+f2dv2+h2dsH22d s^2 =-d u^2 + f^2 d v^2 +h^2 d s^2_{H^2}, where ff and hh are the functions of uu and dsH22d s^2_{H^2} is the metric on the two-dimensional hyperbolic space H2H^2. We show that in the adiabatic limit, when the metric on H2H^2 is scaled down, the Yang-Mills equations become the sigma-model equations describing harmonic maps from a two-dimensional manifold (dS2_2, AdS2_2 or R1,1R^{1,1}, respectively) into the based loop group ΩG=C∞(S1,G)/G\Omega G=C^\infty (S^1, G)/G of smooth maps from the boundary circle S1=∂H2S^1=\partial H^2 of H2H^2 into the gauge group GG. From this correspondence and the implicit function theorem it follows that the moduli space of Yang-Mills theory with a gauge group GG in four dimensions is bijective to the moduli space of two-dimensional sigma model with ΩG\Omega G as the target space. The sigma-model field equations can be reduced to equations of geodesics on ΩG\Omega G, solutions of which yield magnetic-type configurations of Yang-Mills fields. The group ΩG\Omega G naturally acts on their moduli space.Comment: 8 pages; v3: clarifying remarks and references adde
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