3 citations · 11 across the 18 of their papers we have counts for
9 papers · 1 filter
Complexes of strong discrete Morse matchings
Kevin Knudson, Abigail Owens-White
Using the strong discrete Morse theory developed by Fernández, we define the complex of strong discrete Morse matchings on a simplicial complex , as well as th…
Approximate triangulations of Grassmann manifolds
Kevin P. Knudson
We define the notion of an approximate triangulation for a manifold embedded in euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertic…
Min-max theory for cell complexes
Lacey Johnson, Kevin Knudson
In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. In this paper we introduce a discretized version o…
Theoretical Geometry, Critical Theory, and Concept Spaces in IR
Laura Sjoberg, Kevin Knudson
We use the theory of persistent homology to analyze a data set arising from the study of various aspects of democracy. Our results show that most "mature" democracies look more or…
Birth and death in discrete Morse theory
Henry King, Kevin Knudson, Neza Mramor
Suppose is a finite simplicial complex and that for we have a discrete Morse function $F_{t_i}:M\to \zr$. In this paper, we study the births and deaths of…
A refinement of multi-dimensional persistence
Kevin P. Knudson
We study the multi-dimensional persistence of Carlsson and Zomorodian and obtain a finer classification based upon the higher tor-modules of a persistence module. We propose a vari…