1 citations · 1 across the 4 of their papers we have counts for
4 papers
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…
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…
A theorem of Retakh for exact -categories and higher extension functors
Erlend D. Børve, Paul Trygsland
We define extension -categories for exact -categories in terms of bifibrations. Extension -categories are invariant when passing to the stable hull, and con…
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…