Hochschild homology, and a persistent approach via connectivity digraphs
| Autor: | Caputi, Luigi, Riihimäki, Henri |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Applied and Computational Topology (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s41468-023-00118-9 |
| Popis: | We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\geq 2$. To extend them to higher degrees, we introduce the notion of connectivity digraphs and analyse two main examples; the first, arising from Atkin's $q$-connectivity, and the second, here called $n$-path digraphs, generalising the classical notion of line graphs. Based on a categorical setting for persistent homology, we propose a stable pipeline for computing persistent Hochschild homology groups. This pipeline is also amenable to other homology theories; for this reason, we complement our work with a survey on homology theories of digraphs. Comment: Comments are welcome! |
| Databáze: | arXiv |
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