7 citations · 10 across the 19 of their papers we have counts for
4 papers · 1 filter
Merge trees in discrete Morse theory
Benjamin Johnson, Nicholas A. Scoville
In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and d…
Higher connectivity of the Morse complex
Nicholas A. Scoville, Matthew C. B. Zaremsky
The Morse complex of a finite simplicial complex is the complex of all gradient vector fields on . In this paper we study higher connectivity properties of…
The Digital Hopf Construction
Gregory Lupton, John Oprea, Nicholas A. Scoville
Various concepts and constructions in homotopy theory have been defined in the digital setting. Although there have been several attempts at a definition of a fibration in the digi…
Fundamental Theorems of Morse Theory on posets
D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera Lois +2
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse t…