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Hochschild homology, and a persistent approach via connectivity digraphs

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Main Authors: Luigi, Caputi, Henri, Riihimäki
Format: Book
Language:English
Published: Springer 2023
Subjects:
persistent Hochschild homology framework
Atkin’s q-connectivity
Online Access:https://link.springer.com/article/10.1007/s41468-023-00118-9
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7660
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spelling oai:localhost:PNK-76602023-04-06T09:50:56Z Hochschild homology, and a persistent approach via connectivity digraphs Luigi, Caputi Henri, Riihimäki persistent Hochschild homology framework Atkin’s q-connectivity CC BY We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree i≥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 graph. 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 directed graphs. 2023-04-06T09:50:56Z 2023-04-06T09:50:56Z 2023 Book https://link.springer.com/article/10.1007/s41468-023-00118-9 https://dlib.phenikaa-uni.edu.vn/handle/PNK/7660 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic persistent Hochschild homology framework
Atkin’s q-connectivity
spellingShingle persistent Hochschild homology framework
Atkin’s q-connectivity
Luigi, Caputi
Henri, Riihimäki
Hochschild homology, and a persistent approach via connectivity digraphs
description CC BY
format Book
author Luigi, Caputi
Henri, Riihimäki
author_facet Luigi, Caputi
Henri, Riihimäki
author_sort Luigi, Caputi
title Hochschild homology, and a persistent approach via connectivity digraphs
title_short Hochschild homology, and a persistent approach via connectivity digraphs
title_full Hochschild homology, and a persistent approach via connectivity digraphs
title_fullStr Hochschild homology, and a persistent approach via connectivity digraphs
title_full_unstemmed Hochschild homology, and a persistent approach via connectivity digraphs
title_sort hochschild homology, and a persistent approach via connectivity digraphs
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s41468-023-00118-9
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7660
_version_ 1762456096059949056
score 8.893527

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