Titlebook: Geometry and Dynamics of Groups and Spaces; In Memory of Alexand Mikhail Kapranov,Yuri Ivanovich Manin,Leonid Potya Book 2008 Birkhäuser Ba

宣誓书

Pentagon Relation for the Quantum Dilogarithm and Quantized ,,rove that it is preserved by the intertwiner operator defined using the quantum dilogarithm. Using this we can define a representation of the quantized moduli space of configurations of 5 points on the projective line.

Minutes

Geodesic Flow on the Normal Congruence of a Minimal Surfaces. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ℝ. and relate it to the classical Weierstrass representation.

intolerance

Milnor Invariants and ,-Class Groupsic Milnor numbers. As an application, we describe the Galois module structure of the .-class group of a cyclic extension of ℚ of degree . (. being a prime number) in terms of the arithmetic higher linking matrices. In particular, our formula generalizes the classical formula of Rédei on the 4 and 8 ranks of the 2-class group of a quadratic field.

extinct

https://doi.org/10.1007/978-3-662-36809-1Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. In this paper we generalise this to the case of groups of Möbius transformations of a non-Archimedean metric space. As an application, we give a version of Jørgensen’s inequality for SL(2, ℚ.).

hermitage

Reservation

智力高

IST

https://doi.org/10.1007/978-3-642-86505-3This is a survey of higher-dimensional Kleinian groups, i.e., discrete isometry groups of the hyperbolic .-space ℍ. for . ≥ 4. Our main emphasis is on the topological and geometric aspects of higher-dimensional Kleinian groups and their contrast with the discrete groups of isometry of ℍ..

Petechiae

Inflamed

Chern Character for Twisted ComplexesWe construct the Chern character from the .-theory of twisted perfect complexes of an algebroid stack to the negative cyclic homology of the algebra of twisted matrices associated to the stack.