Last edited by Kajihn
Thursday, August 13, 2020 | History

7 edition of Continuous Bounded Cohomology of Locally Compact Groups found in the catalog.

Continuous Bounded Cohomology of Locally Compact Groups

by Nicolas Monod

  • 44 Want to read
  • 34 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Linear algebra,
  • Topology,
  • Theory Of Groups,
  • Homology Theory,
  • Mathematics,
  • Science/Mathematics,
  • Probability & Statistics - General,
  • Locally compact groups,
  • Algebra - Linear,
  • General,
  • Bounded cohomology,
  • Mathematics / Algebra / Linear,
  • Mathematics / Topology,
  • Mathematics-Probability & Statistics - General,
  • Medical-General,
  • continuous cohomology,
  • lattices in Lie groups,
  • Geometry - Algebraic,
  • Group Theory

  • The Physical Object
    FormatPaperback
    Number of Pages214
    ID Numbers
    Open LibraryOL9057284M
    ISBN 103540420541
    ISBN 109783540420545

    Chapter 2. (Bounded) cohomology of groups in low degree 9 26; (Bounded) group cohomology in degree zero and one 9 26; Group cohomology in degree two 9 26; Bounded group cohomology in degree two: quasimorphisms 12 29; Homogeneous quasimorphisms 13 30; Quasimorphisms on abelian groups 14 31; The bounded cohomology of. Bounded cohomology and applications: a panorama Marc Burger Bounded cohomology for groups and spaces is related to usual cohomology and in fact enriches it by providing stronger invariants. The aim of this talk is to illustrate certain aspects of this philosophy. General references for bounded cohomology are [12, 21, 22, 3]. 1. Definition, low.

    Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share . any local eld) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and groups over global elds. We also establish vanishing and cohomological rigidity results for products of general locally compact groups and their lattices. 1.

    Lecture The bounded cohomology group of a group with coefficients in a module can be computed via strong and relatively injective resolution: the isomorphism is biLipschitz; Special strong and relatively injective resolutions compute isometrically bounded cohomology with the canonical seminorm. Bounded cohomology and isometry groups of hyperbolic spaces Received August 5, and in revised form Septem lattice 3in a product G= G1 ×G2 of two locally compact σ-compact and non-compact A cocycle for the action of 8ton Wis a continuous function c: W× R → R such that c(v,s+t)= c(v,t)+c.


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Continuous Bounded Cohomology of Locally Compact Groups by Nicolas Monod Download PDF EPUB FB2

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable.

This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. However, the latter has remained by and large intractable.

This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology.

Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients inBrand: Springer-Verlag Berlin Heidelberg.

Get this from a library. Continuous bounded cohomology of locally compact groups. [Nicolas Monod]. Get this from a library. Continuous bounded cohomology of locally compact groups. [Nicolas Monod] -- Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology.

However, the latter has remained by and large intractable. This monograph introduces the. Continuous bounded cohomology of locally compact groups Monod, Nicolas The purpose of this monograph is (a) to lay the foundations for a conceptual approach to bounded cohomology; (b) to harvest the resulting applications in rigidity theory.

CONTINUOUS BOUNDED COHOMOLOGY AND APPLICATIONS TO RIGIDITY THEORY M. Burger and N. Monod Introduction and Statement of the Results We presenta theory of continuous boundedcohomology of locally compact groups with coefficients in Banach modules. A central rˆole is played by amenable actions, as they give rise to relatively injective resolutions.

In mathematics, a topological group is a group G together with a topology on G such that both the group's binary operation and the function mapping group elements to their respective inverses are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a topological structure.

Thus, one may perform algebraic operations. Abstract. One of the important features of the theory of continuous bounded cohomology is that the bi-functors H• cb come with a natural transformation Ψ •: H• cb → H • c to the continuous cohomology H • c or to the Eilenberg-MacLane cohomology if the group under consideration is discrete.

As a matter of fact, most applications of bounded continuous cohomology. The authors begin with general material, covering Lie algebra cohomology, as well as continuous and differentiable cohomology. Much of the machinery is designed for the study of the cohomology of locally symmetric spaces, realized as double coset spaces, where the quotient is by a maximal compact subgroup and by a discrete subgroup.

1 Introduction. This article is concerned with the boundedness problem in continuous cohomology of Lie groups. Given a Lie group G and a class α in the continuous cohomology of G with real coefficients, one may investigate whether α can be represented by a bounded cocycle.

This question may be reformulated in more invariant terms by asking whether α is contained in the image of the. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. A theory of continuous bounded cohomology for locally compact groups was deve-loped in [27] and this proved itself to be rather useful and flexible at the same time.

Bounded cohomology was originally defined by Gromov in and has already been used by several authors. The point of the theory developed in [27] is the introduc. Let [Fraktur capital]A be a Banach algebra, [Fraktur capital]X a two-sided Banach [Fraktur capital] A-module, and define the cohomology groups [italic]H[italic superscript]n([Fraktur capital]A, [Fraktur capital]X) from the complex of bounded cochains in exact analogy to the classical (algebraic) case.

This article gives an introduction to several aspects of the resulting theory. This paper has been withdrawn by the author. It was announced me that there is a very advanced book: "Nicolas Monod, Continuous bounded cohomology of locally compact groups".

I found that many results of my paper on topological semigroups are simple generalizations of the results of Monod's book. So, I withdraw the paper: Subjects. Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. Armand Borel, Nolan R.

Wallach. American Mathematical Soc., - Mathematics - pages. a locally compact group we (ab)use the same notations H∗,H∗ b for the continuous (bounded) cohomology; for present purposes, it is simply defined by requiring that all cochains be continuous1.

I will mainly concentrate on the group case; a theorem of M. Gromov of funda. Continuous bounded cohomology of locally compact groups. Berlin: Springer, (DLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Nicolas Monod.

compact extension of a simple Lie group Lof rank one, and there is a continuous surjective homomorphism G→ L.

The proof of this result uses second bounded cohomology for closed subgroups of the isometry group Iso(X) of X. Here the second bounded cohomology group of a locally compact topological group Gwith coeffients in a Banach module Efor. Our theory can be considered as a topological version of bounded cohomology of discrete t: This paper has been withdrawn by the author.

It was announced me that there is a very advanced book: "Nicolas Monod, Continuous bounded cohomology of locally compact groups". Bounded cohomology has been an important tool in geometric group theory and rigidity theory ever since its introduction by Gromov in The definition of continuous bounded cohomology in by Burger and Monod has led to the study of bounded cohomology of lattices in Lie groups with many new and unexpected applications, in particular in.5.

Differentiable cohomology and continuous cohomology for Lie groups ; 6. Further results on differentiable cohomology ; Chapter X. Continuous and Differentiable Cohomology for Locally Compact Totally Disconnected Groups ; 1.

Continuous and smooth cohomology ; 2. Cohomology of reductive groups and buildings ; 3.Abstract. In order to illustrate some of the machinery of continuous bounded cohomology, we work out a couple of concrete questions in the particular case of SL we compute, in degree two, the continuous bounded cohomology of SL 2 (ℝ) with unitary irreducible coefficients.

Then we explore the connections between dilogarithm functions and the continuous bounded cohomology of SL 2 (ℝ.