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 furthermore it includes an influential, thus far unpublished manuscript of Reznikov of ebook size.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
Similar differential geometry books
The Surveys in Differential Geometry are supplementations to the magazine of Differential Geometry, that are released through overseas Press. They contain major invited papers combining unique examine and overviews of the most up-tp-date study in particular parts of curiosity to the starting to be magazine of Differential Geometry neighborhood.
Necessary transforms, reminiscent of the Laplace and Fourier transforms, were significant instruments in arithmetic for a minimum of centuries. within the final 3 a long time the advance of a few novel rules in algebraic geometry, classification conception, gauge concept, and string conception has been heavily with regards to generalizations of quintessential transforms of a extra geometric personality.
Aus dem Vorwort: "Globale Probleme der Differentialgeometrie erfreuen sich eines immer noch wachsenden Interesses. Gerade in der Riemannschen Geometrie hat die Frage nach Beziehungen zwischen Riemannscher und topologischer Struktur in neuerer Zeit zu vielen sch? nen und ? berraschenden Einsichten gef?
This ebook brings into concentration the synergistic interplay among research and geometry through reading various subject matters in functionality concept, genuine research, harmonic research, numerous advanced variables, and crew activities. Krantz's technique is prompted by means of examples, either classical and glossy, which spotlight the symbiotic dating among research and geometry.
- Differentiable Manifolds
- The Breadth of Symplectic and Poisson Geometry: Festschrift in Honor of Alan Weinstein
- Streifzüge durch die Kontinuumstheorie
- The Method of Equivalence and Its Applications
- Modern Geometry— Methods and Applications: Part II: The Geometry and Topology of Manifolds
Additional resources for Geometry and dynamics of groups and spaces: In memory of A.Reznikov
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], , that this space coincides with Wps (and not Hps ).