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arXiv · 2105.08698

Higher-degree bounded cohomology of transformation groups

Martin Nitsche
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Abstract

For $M$ a compact Riemannian manifold Brandenbursky and Marcinkowski constructed a transfer map $H_b^*(π_1(M))\to H_b^*(Homeo_{vol,0}(M))$ and used it to show that for certain $M$ the space $\overline{EH}_b^3(Homeo_{vol,0}(M))$ is infinite-dimensional. Kimura adapted the argument to $Diff_{vol}(D^2,\partial D^2)$. We extend both results to the higher degrees $\overline{EH}_b^{2n}$, $n\geq 1$. We also show that for certain $M$ the ordinary cohomology $H^*(Homeo_{vol,0}(M))$ is non-trivial in all degrees. In our computations we view the transfer map as being induced by a coupling of groups.

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Martin Nitsche. 2021-05-18. Higher-degree bounded cohomology of transformation groups. https://arxiv.org/abs/2105.08698

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