Pairings, duality, amenability and bounded cohomology

Jacek Brodzki; Graham A. Niblo; Nick J. Wright

Journal of the European Mathematical Society (2012)

  • Volume: 014, Issue: 5, page 1513-1518
  • ISSN: 1435-9855

Abstract

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We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.

How to cite

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Brodzki, Jacek, Niblo, Graham A., and Wright, Nick J.. "Pairings, duality, amenability and bounded cohomology." Journal of the European Mathematical Society 014.5 (2012): 1513-1518. <http://eudml.org/doc/277288>.

@article{Brodzki2012,
abstract = {We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.},
author = {Brodzki, Jacek, Niblo, Graham A., Wright, Nick J.},
journal = {Journal of the European Mathematical Society},
keywords = {amenability; group cohomology; bounded cohomology; uniformly finite homology; invariant means; amenability; group cohomology; bounded cohomology; uniformly finite homology; invariant means},
language = {eng},
number = {5},
pages = {1513-1518},
publisher = {European Mathematical Society Publishing House},
title = {Pairings, duality, amenability and bounded cohomology},
url = {http://eudml.org/doc/277288},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Brodzki, Jacek
AU - Niblo, Graham A.
AU - Wright, Nick J.
TI - Pairings, duality, amenability and bounded cohomology
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 5
SP - 1513
EP - 1518
AB - We give a new perspective on the homological characterizations of amenability given by Johnson & Ringrose in the context of bounded cohomology and by Block & Weinberger in the context of uniformly finite homology. We examine the interaction between their theories and explain the relationship between these characterizations. We apply these ideas to give a new proof of non-vanishing for the bounded cohomology of a free group.
LA - eng
KW - amenability; group cohomology; bounded cohomology; uniformly finite homology; invariant means; amenability; group cohomology; bounded cohomology; uniformly finite homology; invariant means
UR - http://eudml.org/doc/277288
ER -

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