Double, über and poset homology

We present a comparison map between the uberhomology of a simplicial complex $\mathcal{K}$ and the double homology of its associated moment-angle complex $\mathcal{Z}_{\mathcal{K}}$. We show these two homology theories differ at three bidegrees, which depend on whether the complex $K$ is neighbourly or not.

Publication Details

Journal
arXiv (Cornell University)
Published
2025-10-12
Primary Topic
Geomagnetism and Paleomagnetism Studies
Type
article
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article

Double, über and poset homology

arXiv (Cornell University)
Geomagnetism and Paleomagnetism Studies
article

Double, über and poset homology

article en

Abstract

We present a comparison map between the uberhomology of a simplicial complex $\mathcal{K}$ and the double homology of its associated moment-angle complex $\mathcal{Z}_{\mathcal{K}}$. We show these two homology theories differ at three bidegrees, which depend on whether the complex $K$ is neighbourly or not.

arXiv (Cornell University)
Reduced inequalities
Openalex Percentile: Top 44%
Geomagnetism and Paleomagnetism Studies
Open Access PDFOpenAlex
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Double, über and poset homology · arXiv (Cornell University) (2025) | TGRS Research Map | TGRS