43 citations · 238 across the 28 of their papers we have counts for
9 papers · 1 filter
Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
Henry Adams, Sushovan Majhi, Fedor Manin +2
Let be a finite, connected metric graph and let be a subset. If is sufficiently dense in , we show that the Gromov--Hausdorff distance matches the Hausdor…
Contractibility of the Rips complexes of Integer lattices via local domination
Žiga Virk
We prove that for each positive integer , the Rips complexes of the -dimensional integer lattice in the metric (i.e., the Manhattan metric, also called the natural word…
On the metric spaces of lattices and periodic point sets
Alexey Garber, Žiga Virk, Nicolò Zava
Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals.…
Vietoris thickenings and complexes have isomorphic homotopy groups
Henry Adams, Florian Frick, Žiga Virk
We study the relationship between metric thickenings and simplicial complexes associated to coverings of metric spaces. Let be a cover of a separable metric space …
Rips complexes as nerves and a Functorial Dowker-Nerve Diagram
Žiga Virk
Using ideas of the Dowker duality we prove that the Rips complex at scale is homotopy equivalent to the nerve of a cover consisting of sets of prescribed diameter. We then deve…
The Space of Persistence Diagrams on Points Coarsely Embeds into Hilbert Space
Atish Mitra, Žiga Virk
We prove that the space of persistence diagrams on points (with the bottleneck or a Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic dime…