Stratified formal deformations and intersection homology of data point clouds

Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes under which intersection homology remains invariant. In part...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Banagl, Markus (VerfasserIn) , Mäder, Tim (VerfasserIn) , Sadlo, Filip (VerfasserIn)
Dokumenttyp: Article (Journal) Kapitel/Artikel
Sprache:Englisch
Veröffentlicht: 25 May 2020
In: Arxiv
Year: 2020, Pages: 1-22
DOI:10.48550/arXiv.2005.11985
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2005.11985
Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2005.11985
Volltext
Verfasserangaben:Markus Banagl, Tim Mäder, and Filip Sadlo

MARC

LEADER 00000caa a2200000 c 4500
001 1818129094
003 DE-627
005 20230118164530.0
007 cr uuu---uuuuu
008 221006s2020 xx |||||o 00| ||eng c
024 7 |a 10.48550/arXiv.2005.11985  |2 doi 
035 |a (DE-627)1818129094 
035 |a (DE-599)KXP1818129094 
035 |a (OCoLC)1361714625 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 29  |2 sdnb 
100 1 |a Banagl, Markus  |d 1971-  |e VerfasserIn  |0 (DE-588)132548232  |0 (DE-627)658065114  |0 (DE-576)185904351  |4 aut 
245 1 0 |a Stratified formal deformations and intersection homology of data point clouds  |c Markus Banagl, Tim Mäder, and Filip Sadlo 
264 1 |c 25 May 2020 
300 |a 22 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 06.10.2022 
520 |a Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes under which intersection homology remains invariant. In particular, we obtain the notions of stratified formal deformations and stratified spines of a complex, leading to reductions of complexes prior to computation of intersection homology. We implemented the algorithmic execution of such transformations, as well as the calculation of intersection homology, and apply these algorithms to investigate the intersection homology of stratified spines in Vietoris-Rips type complexes associated to point sets sampled near given, possibly singular, spaces. 
650 4 |a 55N33, 68 
650 4 |a Computer Science - Computational Geometry 
650 4 |a Mathematics - Algebraic Topology 
700 1 |a Mäder, Tim  |d 1994-  |e VerfasserIn  |0 (DE-588)1269864637  |0 (DE-627)1818269449  |4 aut 
700 1 |a Sadlo, Filip  |d 1972-  |e VerfasserIn  |0 (DE-588)1116552744  |0 (DE-627)871226030  |0 (DE-576)478485913  |4 aut 
773 0 8 |i Enthalten in  |t Arxiv  |d Ithaca, NY : Cornell University, 1991  |g (2020), Artikel-ID 2005.11985, Seite 1-22  |h Online-Ressource  |w (DE-627)509006531  |w (DE-600)2225896-6  |w (DE-576)28130436X  |7 nnas  |a Stratified formal deformations and intersection homology of data point clouds 
773 1 8 |g year:2020  |g elocationid:2005.11985  |g pages:1-22  |g extent:22  |a Stratified formal deformations and intersection homology of data point clouds 
856 4 0 |u https://doi.org/10.48550/arXiv.2005.11985  |x Verlag  |x Resolving-System  |z lizenzpflichtig  |3 Volltext 
856 4 0 |u http://arxiv.org/abs/2005.11985  |x Verlag  |z lizenzpflichtig  |3 Volltext 
951 |a AR 
992 |a 20221006 
993 |a Article 
994 |a 2020 
998 |g 1116552744  |a Sadlo, Filip  |m 1116552744:Sadlo, Filip  |d 700000  |d 741000  |d 741030  |d 700000  |d 728500  |e 700000PS1116552744  |e 741000PS1116552744  |e 741030PS1116552744  |e 700000PS1116552744  |e 728500PS1116552744  |k 0/700000/  |k 1/700000/741000/  |k 2/700000/741000/741030/  |k 0/700000/  |k 1/700000/728500/  |p 3  |y j 
998 |g 1269864637  |a Mäder, Tim  |m 1269864637:Mäder, Tim  |d 700000  |d 728500  |e 700000PM1269864637  |e 728500PM1269864637  |k 0/700000/  |k 1/700000/728500/  |p 2 
998 |g 132548232  |a Banagl, Markus  |m 132548232:Banagl, Markus  |d 110000  |d 110100  |d 110000  |d 110400  |d 700000  |d 728500  |e 110000PB132548232  |e 110100PB132548232  |e 110000PB132548232  |e 110400PB132548232  |e 700000PB132548232  |e 728500PB132548232  |k 0/110000/  |k 1/110000/110100/  |k 0/110000/  |k 1/110000/110400/  |k 0/700000/  |k 1/700000/728500/  |p 1  |x j 
999 |a KXP-PPN1818129094  |e 4194791010 
BIB |a Y 
JSO |a {"language":["eng"],"recId":"1818129094","type":{"bibl":"chapter","media":"Online-Ressource"},"note":["Gesehen am 06.10.2022"],"title":[{"title":"Stratified formal deformations and intersection homology of data point clouds","title_sort":"Stratified formal deformations and intersection homology of data point clouds"}],"person":[{"role":"aut","roleDisplay":"VerfasserIn","display":"Banagl, Markus","given":"Markus","family":"Banagl"},{"role":"aut","display":"Mäder, Tim","roleDisplay":"VerfasserIn","given":"Tim","family":"Mäder"},{"given":"Filip","family":"Sadlo","role":"aut","roleDisplay":"VerfasserIn","display":"Sadlo, Filip"}],"relHost":[{"physDesc":[{"extent":"Online-Ressource"}],"id":{"eki":["509006531"],"zdb":["2225896-6"]},"origin":[{"publisherPlace":"Ithaca, NY ; [Erscheinungsort nicht ermittelbar]","dateIssuedKey":"1991","publisher":"Cornell University ; Arxiv.org","dateIssuedDisp":"1991-"}],"recId":"509006531","language":["eng"],"disp":"Stratified formal deformations and intersection homology of data point cloudsArxiv","type":{"bibl":"edited-book","media":"Online-Ressource"},"note":["Gesehen am 28.05.2024"],"part":{"extent":"22","text":"(2020), Artikel-ID 2005.11985, Seite 1-22","pages":"1-22","year":"2020"},"titleAlt":[{"title":"Arxiv.org"},{"title":"Arxiv.org e-print archive"},{"title":"Arxiv e-print archive"},{"title":"De.arxiv.org"}],"pubHistory":["1991 -"],"title":[{"title":"Arxiv","title_sort":"Arxiv"}]}],"physDesc":[{"extent":"22 S."}],"id":{"doi":["10.48550/arXiv.2005.11985"],"eki":["1818129094"]},"origin":[{"dateIssuedDisp":"25 May 2020","dateIssuedKey":"2020"}],"name":{"displayForm":["Markus Banagl, Tim Mäder, and Filip Sadlo"]}} 
SRT |a BANAGLMARKSTRATIFIED2520