PreprintCC BY-NC-ND 4.0arXiv
Bounded cohomology, Codimension two submanifolds and Pontryagin-Thom constructions
Abstract
In this note we develop a novel approach for proving the non-vanishing of bounded cohomology. This utilizes a splitting argument whose simplest form is as follows: Let M denote an n-manifold of non-zero simplicial volume and N a codimension two submanifold of M, then one can conclude that the n-th bounded cohomology of the fundamental group of M \ N is non-zero. We then translate the existence of a complement with a given fundamental group into an easily accessible homology computation, which might be of independent interest.
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BibTeX
@misc{kastenholz2026bounded,
title = {{Bounded cohomology, Codimension two submanifolds and Pontryagin-Thom constructions}},
author = {Thorben Kastenholz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27476},
eprint = {2609.27476},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27476},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bounded cohomology, Codimension two submanifolds and Pontryagin-Thom constructions
AU - Thorben Kastenholz
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27476
UR - https://arxiv.org/abs/2609.27476
AB - In this note we develop a novel approach for proving the non-vanishing of bounded cohomology. This utilizes a splitting argument whose simplest form is as follows: Let M denote an n-manifold of non-zero simplicial volume and N a codimension two submanifold of M, then one can conclude that the n-th bounded cohomology of the fundamental group of M \ N is non-zero. We then translate the existence of a complement with a given fundamental group into an easily accessible homology computation, which might be of independent interest.
ER -