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Displacement techniques in bounded cohomology

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Peer-reviewed

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https://www.repository.cam.ac.uk/handle/1810/380445

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Article

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Authors

Fournier-Facio, F  ORCID logo  https://orcid.org/0000-0003-0386-2071

Abstract

Abstract Several algebraic criteria, reflecting displacement properties of transformation groups, have been used in the past years to prove vanishing of bounded cohomology and stable commutator length. Recently, the authors introduced the property of commuting cyclic conjugates, a new displacement technique that is widely applicable and provides vanishing of the bounded cohomology in all positive degrees and all dual separable coefficients. In this note we consider the most recent along with the by now classical displacement techniques and we study implications among them as well as counterexamples.

Description

Acknowledgements: CC acknowledges support by the European Union in the form of a María Zambrano grant. FFF was supported by the Herchel Smith Postdoctoral Fellowship Fund. YL was partially supported by the NSF CAREER award 2240136. MM was partially supported by the INdAM–GNSAGA Project CUP E55F22000270001 and by the ERC “Definable Algebraic Topology" DAT - Grant Agreement n. 101077154. CC, FFF and YL thank also the Instituto de Ciencias Matemáticas (ICMAT) for its hospitality during the Thematic program on geometric group theory and low-dimensional geometry and topology (May-July 2023), where part of this research was conducted. MM also thanks the Forschungsinstitut für Mathematik (ETH Zürich) for its hospitality, where part of this research was conducted. This work has been supported by the Madrid Government (Comunidad de Madrid - Spain) under the multiannual Agreement with UAM in the line for the Excellence of the University Research Staff in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). This work has been funded by the European Union - NextGenerationEU under the National Recovery and Resilience Plan (PNRR) - Mission 4 Education and research - Component 2 From research to business - Investment 1.1 Notice Prin 2022 - DD N. 104 del 2/2/2022, with title “Geometry and topology of manifolds", proposal code 2022NMPLT8 - CUP J53D23003820001.

Keywords

4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

Manuscripta Mathematica

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Journal ISSN

0025-2611
1432-1785

Volume Title

176

Publisher

Springer Science and Business Media LLC

Publisher DOI

https://doi.org/10.1007/s00229-024-01604-9

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