101,046 research outputs found
Homology and K-theory of the Bianchi groups
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 -homology. By the Baum/Connes
conjecture, which holds for the Bianchi groups, we obtain the -theory of
their reduced -algebras in terms of isomorphic images of the computed
-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
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
We consider the Yang-Mills equations with a matrix gauge group on the de
Sitter dS, anti-de Sitter AdS and Minkowski spaces. On all
these spaces one can introduce a doubly warped metric in the form , where and are the functions of
and is the metric on the two-dimensional hyperbolic space .
We show that in the adiabatic limit, when the metric on is scaled down,
the Yang-Mills equations become the sigma-model equations describing harmonic
maps from a two-dimensional manifold (dS, AdS or ,
respectively) into the based loop group of
smooth maps from the boundary circle of into the gauge
group . From this correspondence and the implicit function theorem it
follows that the moduli space of Yang-Mills theory with a gauge group in
four dimensions is bijective to the moduli space of two-dimensional sigma model
with as the target space. The sigma-model field equations can be
reduced to equations of geodesics on , solutions of which yield
magnetic-type configurations of Yang-Mills fields. The group
naturally acts on their moduli space.Comment: 8 pages; v3: clarifying remarks and references adde
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