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Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory.

In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The research articles broadly reflect the range of Reznikov's own interests in geometry, group and number theory, functional analysis, dynamical systems and topology.

The book further contains an extensive survey "Geometrization of probability", "Kleinian groups in higher dimensions", "(C,F)-construction of funny rank-one actions for locally compact groups", and some articles centering on Reznikov as a person.




Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory.

In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The research articles broadly reflect the range of Reznikov's own interests in geometry, group and number theory, functional analysis, dynamical systems and topology.

The book further contains an extensive survey "Geometrization of probability", "Kleinian groups in higher dimensions", "(C,F)-construction of funny rank-one actions for locally compact groups", and some articles centering on Reznikov as a person.


Content:
Front Matter....Pages i-xxix
Front Matter....Pages 1-1
Analytic Topology of Groups, Actions, Strings and Varieties....Pages 3-93
Front Matter....Pages 95-95
J?rgensen’s Inequality for Non-Archimedean Metric Spaces....Pages 97-111
The Hypoelliptic Dirac Operator....Pages 113-246
Generalized Operads and Their Inner Cohomomorphisms....Pages 247-308
Chern Character for Twisted Complexes....Pages 309-324
(C, F)-Actions in Ergodic Theory....Pages 325-351
Homomorphic Images of Branch Groups, and Serre’s Property (FA)....Pages 353-375
On Nori’s Fundamental Group Scheme....Pages 377-398
The Reidemeister Number of Any Automorphism of a Baumslag-Solitar Group is Infinite....Pages 399-414
Pentagon Relation for the Quantum Dilogarithm and Quantized M 0,5 cyc ....Pages 415-428
Geodesic Flow on the Normal Congruence of a Minimal Surface....Pages 429-438
The Chern Character of a Parabolic Bundle, and a Parabolic Corollary of Reznikov’s Theorem....Pages 439-485
Kleinian Groups in Higher Dimensions....Pages 487-564
A ?-bimodules and Serre A ?-functors....Pages 565-645
Geometrization of Probability....Pages 647-667
Milnor Invariants and l-Class Groups....Pages 669-683
Three Topological Properties of Small Eigenfunctions on Hyperbolic Surfaces....Pages 685-695
Quantum p-adic Spaces and Quantum p-adic Groups....Pages 697-719
Convolution Equations on Lattices: Periodic Solutions with Values in a Prime Characteristic Field....Pages 721-742


Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory.

In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The research articles broadly reflect the range of Reznikov's own interests in geometry, group and number theory, functional analysis, dynamical systems and topology.

The book further contains an extensive survey "Geometrization of probability", "Kleinian groups in higher dimensions", "(C,F)-construction of funny rank-one actions for locally compact groups", and some articles centering on Reznikov as a person.


Content:
Front Matter....Pages i-xxix
Front Matter....Pages 1-1
Analytic Topology of Groups, Actions, Strings and Varieties....Pages 3-93
Front Matter....Pages 95-95
J?rgensen’s Inequality for Non-Archimedean Metric Spaces....Pages 97-111
The Hypoelliptic Dirac Operator....Pages 113-246
Generalized Operads and Their Inner Cohomomorphisms....Pages 247-308
Chern Character for Twisted Complexes....Pages 309-324
(C, F)-Actions in Ergodic Theory....Pages 325-351
Homomorphic Images of Branch Groups, and Serre’s Property (FA)....Pages 353-375
On Nori’s Fundamental Group Scheme....Pages 377-398
The Reidemeister Number of Any Automorphism of a Baumslag-Solitar Group is Infinite....Pages 399-414
Pentagon Relation for the Quantum Dilogarithm and Quantized M 0,5 cyc ....Pages 415-428
Geodesic Flow on the Normal Congruence of a Minimal Surface....Pages 429-438
The Chern Character of a Parabolic Bundle, and a Parabolic Corollary of Reznikov’s Theorem....Pages 439-485
Kleinian Groups in Higher Dimensions....Pages 487-564
A ?-bimodules and Serre A ?-functors....Pages 565-645
Geometrization of Probability....Pages 647-667
Milnor Invariants and l-Class Groups....Pages 669-683
Three Topological Properties of Small Eigenfunctions on Hyperbolic Surfaces....Pages 685-695
Quantum p-adic Spaces and Quantum p-adic Groups....Pages 697-719
Convolution Equations on Lattices: Periodic Solutions with Values in a Prime Characteristic Field....Pages 721-742
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