6 papers · 1 filter
Component-Perfect Multidimensional Discrete Morse Functions
Mehmetcik Pamuk, Hanife Varlı
We introduce the concept of component-perfect multidimensional discrete Morse (MDM) functions on finite regular CW complexes. While perfect discrete Morse functions in the classica…
A Closed Formula for the Interleaving Distance of Rectangle Persistence Modules
Mehmet Ali Batan, Claudia Landi, Mehmetcik Pamuk
We give formulas for calculating the interleaving distance between rectangle persistence modules that depend solely on the geometry of the underlying rectangles. Moreover, we exten…
Contiguity Distance between Simplicial Maps
Ayse Borat, Mehmetcik Pamuk, Tane Vergili
We study properties of contiguity distance between simplicial maps. In particular, we show that simplicial versions of -category and topological complexity are particular cases…
Elementary Methods for Persistent Homotopy Groups
Henry Adams, Mehmet Ali Batan, Mehmetcik Pamuk +1
We study the foundational properties of persistent homotopy groups and develop elementary computational methods for their analysis. Our main theorems are persistent analogues of th…
Homological properties of persistent homology
Hanife Varlı, Yağmur Yılmaz, Mehmetcik Pamuk
We investigate to what extent persistent homology benefits from the properties of the usual homology theory.
Decomposing Perfect Discrete Morse Functions on Connected Sums of 3-manifolds
Neza Mramor Kosta, Mehmetcik Pamuk, Hanife Varli
In this paper, we show that if a closed, connected, oriented 3-manifold M = M1#M2 admits a perfect discrete Morse function, then one can decompose this function as perfect discrete…