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Bounded cohomology of transformation groups

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Abstract

Let M be a complete connected Riemannian manifold of finite volume. We present a new method of constructing classes in bounded cohomology of transformation groups such as \(\hbox {Homeo}_0(M,\mu )\), \(\hbox {Diff}_0(M,\hbox {vol})\) and \(\hbox {Symp}_0(M,\omega )\). As an application we show that for many manifolds (in particular for hyperbolic surfaces) the third bounded cohomology of these groups is infinite dimensional.

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Acknowledgements

Both authors were supported by SFB 1085 “Higher Invariants” funded by Deutsche Forschungsgemeinschaft. The second author was supported by grant Sonatina 2018/28/C/ST1/00542 funded by Narodowe Centrum Nauki.

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Authors and Affiliations

  1. Ben Gurion University of the Negev, Be’er Sheva, Israel

    Michael Brandenbursky

  2. Institute of Mathematics, Polish Academy of Sciences, Wrocław, Poland

    Michał Marcinkowski

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  1. Michael Brandenbursky
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  2. Michał Marcinkowski
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Correspondence to Michael Brandenbursky.

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Communicated by Andreas Thom.

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Brandenbursky, M., Marcinkowski, M. Bounded cohomology of transformation groups. Math. Ann. 382, 1181–1197 (2022). https://doi.org/10.1007/s00208-021-02266-8

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