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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Isoperimetric inequalities for Poincaré duality groups
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by Dawid Kielak and Peter Kropholler PDF
Proc. Amer. Math. Soc. 149 (2021), 4685-4698 Request permission


We show that every oriented $n$-dimensional Poincaré duality group over a $*$-ring $R$ is amenable or satisfies a linear homological isoperimetric inequality in dimension $n-1$. As an application, we prove the Tits alternative for such groups when $n=2$. We then deduce a new proof of the fact that when $n=2$ and $R = \mathbb {Z}$ then the group in question is a surface group.
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Additional Information
  • Dawid Kielak
  • Affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom
  • MR Author ID: 1027989
  • ORCID: 0000-0002-5536-9070
  • Email:
  • Peter Kropholler
  • Affiliation: Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
  • MR Author ID: 203863
  • ORCID: 0000-0001-5460-1512
  • Email:
  • Received by editor(s): August 15, 2020
  • Received by editor(s) in revised form: January 19, 2021, March 8, 2021, and March 17, 2021
  • Published electronically: August 13, 2021
  • Additional Notes: The first author was partly supported by a grant from the German Science Foundation (DFG) within the Priority Programme SPP2026 ‘Geometry at Infinity’. This work had received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant agreement No. 850930
  • Communicated by: David Futer
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 4685-4698
  • MSC (2020): Primary 20J06, 57P10
  • DOI:
  • MathSciNet review: 4310095