| Naslov: | Detecting geodesic circles in hyperbolic surfaces with persistent homology |
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| Avtorji: | ID Jelenc, Blaž (Avtor)
ID Virk, Žiga (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (1,39 MB)
MD5: A163532AAA2E11699930ADF56FFC1BAC
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s13398-024-01699-5
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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. |
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| Ključne besede: | simple closed geodesic, Rips complexes, persistent homology, hyperbolic surfaces, systole |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.04.2025 |
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| Leto izida: | 2025 |
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| Št. strani: | 19 str. |
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| Številčenje: | Vol. 119, iss. 2, [article no.] 32 |
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| PID: | 20.500.12556/DiRROS-21208  |
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| UDK: | 515.1 |
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| ISSN pri članku: | 1578-7303 |
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| DOI: | 10.1007/s13398-024-01699-5 |
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| COBISS.SI-ID: | 222367491 |
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| Datum objave v DiRROS: | 15.01.2025 |
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| Število ogledov: | 32 |
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| Število prenosov: | 15 |
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| Metapodatki: |    |
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