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arXiv · 2103.12137

Vertical configuration spaces and their homology

Andrea Bianchi·Florian Kranhold
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Abstract

We introduce ordered and unordered configuration spaces of 'clusters' of points in an Euclidean space $\mathbb{R}^d$, where points in each cluster satisfy a 'verticality' condition, depending on a decomposition $d=p+q$. We compute the homology in the ordered case and prove homological stability in the unordered case.

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Andrea Bianchi, Florian Kranhold. 2021-03-22. Vertical configuration spaces and their homology. https://doi.org/10.1093/qmath/haab061

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