43 citations · 238 across the 28 of their papers we have counts for
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math.AT2021★ 2 cited
Persistent Homology with Selective Rips complexes detects geodesic circles
Žiga Virk
This paper introduces a method to detect each geometrically significant loop that is a geodesic circle (an isometric embedding of ) and a bottleneck loop (meaning that each of…
math.AT2021★ 12 cited
Fast computation of persistent homology representatives with involuted persistent homology
Matija Čufar, Žiga Virk
Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of homology…
math.AT2021★ 13 cited
Footprints of geodesics in persistent homology
Žiga Virk
Given a metric space and a subspace , we prove can generate various algebraic elements in persistent homology of . We call such elements (algebraic) footprin…