3 papers
math.AT2022
Reeb complexes and topological persistence
Melvin Vaupel, Erik Hermansen, Paul Trygsland
We introduce Reeb complexes in order to capture how generators of homology flow along sections of a real valued continuous function. This intuition suggests a close relation of Ree…
math.AT2022
Section complexes of simplicial height functions
Melvin Vaupel, Erik Hermansen, Paul Trygsland
A theory of sections of simplicial height functions is developed. At the core of this theory lies the section complex, which is assembled from higher section spaces. The latter enc…
math.AT2021
Combinatorial models for topological Reeb spaces
Paul Trygsland
There are two rather distinct approaches to Morse theory nowadays: smooth and discrete. We propose to study a real valued function by assembling all associated sections in a topolo…