Higher-degree bounded cohomology of transformation groups

2021/05/18 by Martin Nitsche, Nitsche, Martin · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2105.08698

openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For M a compact Riemannian manifold Brandenbursky and Marcinkowski constructed a transfer map H_b^*(π₁(M))→ H_b^*(Homeo_vol,0(M)) and used it to show that for certain M the space EH_b³(Homeo_vol,0(M)) is infinite-dimensional. Kimura adapted the argument to Diff_vol(D²,∂ D²). We extend both results to the higher degrees EH_b²ⁿ, n≥ 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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• Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces

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• Bounded cohomology of transformation groups
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• Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups