| Title: | Detecting geodesic circles in hyperbolic surfaces with persistent homology |
|---|
| Authors: | ID Jelenc, Blaž (Author)
ID Virk, Žiga (Author) |
|---|
| Files: |  PDF - Presentation file, download (1,39 MB)
MD5: A163532AAA2E11699930ADF56FFC1BAC
 URL - Source URL, visit https://link.springer.com/article/10.1007/s13398-024-01699-5
|
|---|
| Language: | English |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
|
|---|
| Abstract: | In this paper we provide conditions under which a geodesic circle on a hyperbolic surface admits arbitrarily small geodesically convex neighborhoods. This implies that persistent homology using selective Rips complexes detects the length and the position of such a loop via persistent homology in dimensions one, two, or three. In particular, if a surface has a unique systole, then the systole can always be detected with persistent homology. The existential results of the paper are complemented by the corresponding quantitative treatments which explain the choice of parameters of selective Rips complexes as well as conditions, under which the detection occurs via the standard Rips complexes. In particular, if a surface has a unique systole, then the parameters depend on the first spectral gap in the length spectrum. |
|---|
| Keywords: | simple closed geodesic, Rips complexes, persistent homology, hyperbolic surfaces, systole |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 01.04.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 19 str. |
|---|
| Numbering: | Vol. 119, iss. 2, [article no.] 32 |
|---|
| PID: | 20.500.12556/DiRROS-21208  |
|---|
| UDC: | 515.1 |
|---|
| ISSN on article: | 1578-7303 |
|---|
| DOI: | 10.1007/s13398-024-01699-5 |
|---|
| COBISS.SI-ID: | 222367491 |
|---|
| Publication date in DiRROS: | 15.01.2025 |
|---|
| Views: | 34 |
|---|
| Downloads: | 15 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
