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Exact bounded cohomology of measure-preserving homeomorphism groups of nonorientable hyperbolic manifolds

  • Michael Brandenbursky
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Abstract

Let M be a closed, connected, non-orientable hyperbolic manifold, and let μ be a good measure on M. Denote by Homeo0(M,μ) the identity component of the group of μ-preserving homeomorphisms. For every d≥2, we prove that dimEH̅bd(Homeo0(M,μ))=∞, where EH̅bd denotes reduced exact bounded cohomology in degree d.

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Cite

BibTeXRIS
BibTeX
@misc{brandenbursky2026exact,
  title = {{Exact bounded cohomology of measure-preserving homeomorphism groups of nonorientable hyperbolic manifolds}},
  author = {Michael Brandenbursky},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32475},
  eprint = {2610.32475},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32475},
}
RIS
TY  - UNPB
TI  - Exact bounded cohomology of measure-preserving homeomorphism groups of nonorientable hyperbolic manifolds
AU  - Michael Brandenbursky
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32475
UR  - https://arxiv.org/abs/2610.32475
AB  - Let M be a closed, connected, non-orientable hyperbolic manifold, and let μ be a good measure on M. Denote by Homeo_0(M,μ) the identity component of the group of μ-preserving homeomorphisms. For every d≥2, we prove that dimEH̅_b^d(Homeo_0(M,μ))=∞, where EH̅_b^d denotes reduced exact bounded cohomology in degree d.
ER  -