Your browser does not allow JavaScript!
JavaScript is necessary for the proper functioning of this website. Please enable JavaScript or use a modern browser.
Open Science Slovenia
Open Science
DiKUL
slv
|
eng
Search
Browse
New in RUL
About RUL
In numbers
Help
Sign in
Persistent homology with selective Rips complexes detects geodesic circles
ID
Virk, Žiga
(
Author
)
PDF - Presentation file,
Download
(895,74 KB)
MD5: 3E9CF99EE51F243D5412D4874C1F3CB1
URL - Source URL, Visit
https://link.springer.com/article/10.1007/s00009-024-02706-0
Image galllery
Abstract
This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of $S^1$) and a bottleneck loop (meaning that each of its perturbations increases the length) in a geodesic space using persistent homology. Under fairly mild conditions, we show that such a loop either terminates a 1-dimensional homology class or gives rise to a 2-dimensional homology class in persistent homology. The main tool in this detection technique are selective Rips complexes, new custom made complexes that function as an appropriate combinatorial lens for persistent homology to detect the above mentioned loops. The main argument is based on a new concept of a local winding number, which turns out to be an invariant of certain homology classes.
Language:
English
Keywords:
simple closed geodesic spaces
,
Rips complex
,
persistent homology
,
local winding number
Work type:
Article
Typology:
1.01 - Original Scientific Article
Organization:
FRI - Faculty of Computer and Information Science
Publication status:
Published
Publication version:
Version of Record
Year:
2024
Number of pages:
23 str.
Numbering:
Vol. 21, iss. 6, art. 170
PID:
20.500.12556/RUL-160126
UDC:
515.1
ISSN on article:
1660-5446
DOI:
10.1007/s00009-024-02706-0
COBISS.SI-ID:
204600067
Publication date in RUL:
21.08.2024
Views:
50
Downloads:
5
Metadata:
Cite this work
Plain text
BibTeX
EndNote XML
EndNote/Refer
RIS
ABNT
ACM Ref
AMA
APA
Chicago 17th Author-Date
Harvard
IEEE
ISO 690
MLA
Vancouver
:
Copy citation
Share:
Record is a part of a journal
Title:
Mediterranean journal of mathematics
Shortened title:
Mediterr. j. math.
Publisher:
Springer Nature
ISSN:
1660-5446
COBISS.SI-ID:
13561433
Licences
License:
CC BY 4.0, Creative Commons Attribution 4.0 International
Link:
http://creativecommons.org/licenses/by/4.0/
Description:
This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Projects
Funder:
ARRS - Slovenian Research Agency
Project number:
J1-4001
Name:
Izbrani problemi iz uporabne in računske topologije
Funder:
ARRS - Slovenian Research Agency
Project number:
P1-0292
Name:
Topologija in njena uporaba
Similar documents
Similar works from RUL:
Similar works from other Slovenian collections:
Back