By Alexander Reznikov (auth.), Mikhail Kapranov, Yuri Ivanovich Manin, Pieter Moree, Sergiy Kolyada, Leonid Potyagailo (eds.)

Alexander Reznikov (1960-2003) used to be a super and hugely unique mathematician. This e-book provides 18 articles by way of famous mathematicians and is devoted to his reminiscence.

In addition it includes an influential, to date unpublished manuscript by means of Reznikov of publication size. The study articles generally replicate the diversity of Reznikov's personal pursuits in geometry, team and quantity thought, useful research, dynamical platforms and topology.

The publication additional comprises an in depth survey "Geometrization of probability", "Kleinian teams in greater dimensions", "(C,F)-construction of humorous rank-one activities for in the neighborhood compact groups", and a few articles centering on Reznikov as a person.

**Read or Download Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov PDF**

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**Extra info for Geometry and Dynamics of Groups and Spaces: In Memory of Alexander Reznikov**

**Example text**

5 A volume formula for negatively-curved manifolds . . . . . . . . . 5 Groups of volume-preserving diﬀeomorphisms and the nonlinear superrigidity alternative . . . . . . . . . . . . . . . . . 1 log L2 -twistor spaces . . . . . . . . . . . . . . . . . . . . . . . 2 A new invariant of smooth volume-preserving dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . 3 Non-linear superrigidity alternative .

59). 60 we summarize our knowledge of the functionalanalytic structure coming from hyperbolic 3-manifolds which ﬁber over the circle. 1. 1. Let G be a ﬁnitely generated group. Let K = R, C. Let V be a locally convex topological K-vector space which is a G-module, that is, there is a homomorphism G → Aut(V ). If {gi , i = 1, . . , n} is a ﬁnite generating set of G, then the evaluation n map f → {f (gi )} establishes an injective map Z 1 (G, V ) → i=1 V of the space of (inhomogeneous) 1-cocycles of G in V .

2 Property T for K¨ ahler and quaternionic K¨ ahler groups . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 37 46 51 53 54 57 59 61 62 66 66 67 68 68 72 72 73 74 76 78 79 80 82 83 84 85 85 87 Analytic Topology of Groups, Actions, Strings and Varieties 5 Introduction This paper is devoted to applications of Analysis to Topology. The latter is very broadly understood and includes geometric theory of ﬁnitely generated groups, group cohomology, Kazhdan groups, actions of groups on manifolds, superrigidity, fundamental groups of K¨ ahler and quaternionic K¨ ahler manifolds and conformal ﬁeld theory.