By Mikhail Kapranov, Sergii Kolyada, Yu. I. Manin, Pieter Moree, Leonid Potyagailo

This ebook offers 18 articles by way of fashionable mathematicians, devoted to the reminiscence of Alexander Reznikov (1960-2003), an excellent hugely unique mathematician with extensive mathematical pursuits. furthermore it includes an influential, thus far unpublished manuscript of Reznikov of ebook size. The learn articles widely mirror the diversity of Reznikov's personal pursuits in geometry, team and quantity conception, useful research, dynamical platforms and topology. furthermore, there are surveys "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 Online or Download Geometry and dynamics of groups and spaces: In memory of A.Reznikov PDF**

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**Additional resources for Geometry and dynamics of groups and spaces: In memory of A.Reznikov**

**Sample text**

2 A new invariant of smooth volume-preserving dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . 3 Non-linear superrigidity alternative . . . . . . . . . . . . . . . . 6 K¨ahler and quaternionic K¨ ahler groups . . . . . . . . . . . . . . . . . 1 Rationality of secondary classes of ﬂat bundles over quasiprojective varieties . . . . . . . . . . . . . . . . . . . . . . 2 Property T for K¨ ahler and quaternionic K¨ ahler groups .

We ﬁnd |l(g)(x)| = |ρ(x0 , g −1 x) − ρ(x0 , x)| ≤ |ρ(g −1 x, x)| = ρ(g −1 , 1). So l is a cocycle of G in l∞ (G). If it were trivial, we would have a bounded function f such that Lg F −F = Lg f −f that is, F −f would be invariant, therefore constant, a contradiction. 3. 2. Now let G be amenable. In this case we have a continuous map m l∞ (G) → K ϕ: j=1 given by (f1 , . . , fm ) → G f1 · · · fm . By the integral we mean the left-invariant normalized mean of bounded functions. 3. Let G be a ﬁnitely generated amenable group, let ρj , j = 1, .

See Equivalently, [120, Chapter 3]. One also deﬁnes Hps (Ω) as the space of restrictions of Hps (Rn ) on Ω. For a compact smooth manifold M without boundary (in particular, for the boundary ∂Ω) one easily deﬁnes the spaces Wps (M ) and Hps (M ) [120, Chapter 3] s in Triebel’s notations). (Hps is Fp,2 If M is compact and g a Riemannian metric on M , let g be the corresponding Laplace–Beltrami operator. One can construct the space of Bessel potentials (1 + )−s/2 (Lp (M )). 5], [55], that this space coincides with Wps (and not Hps ).