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Quantitative chain extensions and integral cohomological fillings
Abstract
We develop two methods in quantitative homological algebra: A declarative approach to integral cohomological filling problems and a quantitatively controlled replacement of normed chain complexes by their homology complex. Both methods are connected through so-called chain extensions. As applications, we obtain transparent proofs for uniform integral simplicial cohomological fillings for subdivisions of simplicial complexes, for uniform integral cohomological fillings of certain finite coverings, and for lower bounds of the ℓ1-semi-norm on product spaces.
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BibTeX
@misc{hofmann2026quantitative,
title = {{Quantitative chain extensions and integral cohomological fillings}},
author = {Franziska Hofmann and Clara Loeh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02987},
eprint = {2610.02987},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02987},
}
RIS
TY - UNPB
TI - Quantitative chain extensions and integral cohomological fillings
AU - Franziska Hofmann
AU - Clara Loeh
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02987
UR - https://arxiv.org/abs/2610.02987
AB - We develop two methods in quantitative homological algebra: A declarative approach to integral cohomological filling problems and a quantitatively controlled replacement of normed chain complexes by their homology complex. Both methods are connected through so-called chain extensions. As applications, we obtain transparent proofs for uniform integral simplicial cohomological fillings for subdivisions of simplicial complexes, for uniform integral cohomological fillings of certain finite coverings, and for lower bounds of the ℓ^1-semi-norm on product spaces.
ER -