Tiến Sĩ Orbit equivalence rigidity and bounded cohomology

Thảo luận trong 'Khoa Học Tự Nhiên' bắt đầu bởi Củ Đậu Đậu, 2/4/14.

  1. Củ Đậu Đậu

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    Abstract
    We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations.
    Our rigidity statements hold for a wide (uncountable) class of groups arising
    from negative curvature geometry. Amongst our applications are (a) measurable Mostow-type rigidity theorems for products of negatively curved groups;
    (b) prime factorization results for measure equivalence; (c) superrigidity for
    orbit equivalence; (d) the first examples of continua of typeII1 equivalence
    relations with trivial outer automorphism group that are mutually not stably
    isomorphic.
    Contents
    1. Introduction
    2. Discussion and applications of the main results
    3. Background in bounded cohomology
    4. Cohomological induction through couplings
    5. Strong rigidity
    6. Superrigidity
    7. Groups in the classCand ME invariants
    References
     

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