Geometry and Dynamics of Groups and Spaces: In Memory of by Alexander Reznikov (auth.), Mikhail Kapranov, Yuri Ivanovich

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 ebook provides 18 articles by means of famous mathematicians and is devoted to his reminiscence.

In addition it comprises an influential, to date unpublished manuscript via Reznikov of e-book size. The examine articles generally replicate the diversity of Reznikov's personal pursuits in geometry, workforce and quantity concept, useful research, dynamical structures and topology.

The publication additional comprises an in depth survey "Geometrization of probability", "Kleinian teams in larger 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.

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

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3 Geometry of unitary cocycles . . . . . . . . . . . . . . . . . . . . . . 1 Smooth and combinatorial harmonic sections . . . . . . . . . . . 2 A convexity theorem . . . . . . . . . . . . . . . . . . . . . . . 3 Cocycle growth for a surface group . . . . . . . . . . . . . . . . 4 A theory of groups of symplectomorphisms . . . . . . . . . . . . . . . 1 Deformation quantization: an overview .

Thus, if ψc = 0 we may assume ψc is a probability measure. Second, let G be the center of gravity map from the nonatomic measures on ∂ N to N [36]. Then G ◦ φc is a π1 (M )-equivariant map from ∂ M to N . In particular, ρ(G ◦ ψc (x), G ◦ ψc (y)) is a π1 (M )-invariant function on ∂ M × ∂ M whence a constant by [54] and [118]. It follows easily that G ◦ ψc = const which is impossible since ρ is discrete. So ψc = 0. ∞ We deduce that ψ is atomic, ψ(z) = i=1 mi δ(ψi (z)), m1 ≥ m2 ≥ · · · . Though ψi (z) : ∂ M → ∂ N are not uniquely defined, mi : ∂ M → R are.

12 Hp,g as operator spaces and the vacuum vector . . . . . . . . . . 13 Equivariant mappings of the Teichm¨ uller Space, the space of quasifuchsian representations and the space of all discrete representations, into Hp,g . . . . . . . . . . . . . . 2 Theory of groups acting on the circle . . . . . . . . . . . . . . . . . . 1 Fundamental cocycle . . . . . . . . . . . . . . . . . . . . . . . 2 Construction of N = 2 quantum fields with lattice symmetry .

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