20.500.12556/RUL-166525 Detecting geodesic circles in hyperbolic surfaces with persistent homology 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. simple closed geodesic Rips complexes persistent homology hyperbolic surfaces systole true false true Angleški jezik Ni določen Članek v reviji 2025-01-17 05:02:55 2025-01-20 13:58:02 2025-01-21 03:59:12 0000-00-00 00:00:00 2025 0 0 19 str. iss. 2, art. 32 Vol. 119 Apr. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.1 1578-7303 10.1007/s13398-024-01699-5 222367491 s13398-024-01699-5.pdf s13398-024-01699-5.pdf 1 5D129814440D93AF9FE875AA2D05229A 311bf6471380b72f35a37e2c9e2267db8a28e3993be009dc9cc617c6c1a818f3 8ce5db32-d72d-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=198405 https://link.springer.com/article/10.1007/s13398-024-01699-5 1 308b3f4a-d487-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=198195 Fakulteta za matematiko in fiziko Fakulteta za računalništvo in informatiko 0 0 0