The fiber of persistent homology for trees

The fiber of persistent homology for trees

Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is $D$. We find that each component is homoto...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Beers, David, Leygonie, Jacob
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Topology
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Beers, David
Leygonie, Jacob
description Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is $D$. We find that each component is homotopy equivalent to a configuration space on $X$ with specialized constraints encoded by the merge tree. For barcodes $D$ with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.
doi_str_mv 10.48550/arxiv.2303.16176
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2303_16176</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2303_16176</sourcerecordid><originalsourceid>FETCH-LOGICAL-a676-31b7b58a74d05423e7b857d1d9eba7107717eb9645e47572d86b104323981eab3</originalsourceid><addsrcrecordid>eNotzrsKwjAUgOEsDqI-gJOZhdac5nLSUcQbCC7dS0JPtdAaSYvo24uX6d9-PsbmIFJltRYrF5_NI82kkCkYQDNmy-JKvG48RR5qfqfYN_1At4FfQxfacHnxOkQ-RKJ-yka1a3ua_TthxW5bbA7J6bw_btanxBk0iQSPXluHqhJaZZLQW40VVDl5hyAQAcnnRmlSqDGrrPEglMxkboGclxO2-G2_2PIem87FV_lBl1-0fAMu_Dqu</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The fiber of persistent homology for trees</title><source>arXiv.org</source><creator>Beers, David ; Leygonie, Jacob</creator><creatorcontrib>Beers, David ; Leygonie, Jacob</creatorcontrib><description>Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is $D$. We find that each component is homotopy equivalent to a configuration space on $X$ with specialized constraints encoded by the merge tree. For barcodes $D$ with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.</description><identifier>DOI: 10.48550/arxiv.2303.16176</identifier><language>eng</language><subject>Mathematics - Algebraic Topology</subject><creationdate>2023-03</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,781,886</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2303.16176$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2303.16176$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Beers, David</creatorcontrib><creatorcontrib>Leygonie, Jacob</creatorcontrib><title>The fiber of persistent homology for trees</title><description>Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is $D$. We find that each component is homotopy equivalent to a configuration space on $X$ with specialized constraints encoded by the merge tree. For barcodes $D$ with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.</description><subject>Mathematics - Algebraic Topology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwjAUgOEsDqI-gJOZhdac5nLSUcQbCC7dS0JPtdAaSYvo24uX6d9-PsbmIFJltRYrF5_NI82kkCkYQDNmy-JKvG48RR5qfqfYN_1At4FfQxfacHnxOkQ-RKJ-yka1a3ua_TthxW5bbA7J6bw_btanxBk0iQSPXluHqhJaZZLQW40VVDl5hyAQAcnnRmlSqDGrrPEglMxkboGclxO2-G2_2PIem87FV_lBl1-0fAMu_Dqu</recordid><startdate>20230328</startdate><enddate>20230328</enddate><creator>Beers, David</creator><creator>Leygonie, Jacob</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230328</creationdate><title>The fiber of persistent homology for trees</title><author>Beers, David ; Leygonie, Jacob</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-31b7b58a74d05423e7b857d1d9eba7107717eb9645e47572d86b104323981eab3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Algebraic Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Beers, David</creatorcontrib><creatorcontrib>Leygonie, Jacob</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Beers, David</au><au>Leygonie, Jacob</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The fiber of persistent homology for trees</atitle><date>2023-03-28</date><risdate>2023</risdate><abstract>Consider the space of continuous functions on a geometric tree $X$ whose persistent homology gives rise to a finite generic barcode $D$. We show that there are exactly as many path connected components in this space as there are merge trees whose barcode is $D$. We find that each component is homotopy equivalent to a configuration space on $X$ with specialized constraints encoded by the merge tree. For barcodes $D$ with either one or two intervals, our method also allows us to compute the homotopy type of this space of functions.</abstract><doi>10.48550/arxiv.2303.16176</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2303.16176
ispartof
issn
language eng
recordid cdi_arxiv_primary_2303_16176
source arXiv.org
subjects Mathematics - Algebraic Topology
title The fiber of persistent homology for trees
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-12T12%3A58%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20fiber%20of%20persistent%20homology%20for%20trees&rft.au=Beers,%20David&rft.date=2023-03-28&rft_id=info:doi/10.48550/arxiv.2303.16176&rft_dat=%3Carxiv_GOX%3E2303_16176%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true