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Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov +5
Given a relation between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…
The bifiltration of a relation and extended Dowker duality
Melvin Vaupel, Benjamin Dunn
We explain how homotopical information of two composeable relations can be organized in two simplicial categories that augment the relations row and column complexes. We show that…
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…