54 citations · 312 across the 36 of their papers we have counts for
7 papers · 1 filter
Directed Homology and Persistence Modules
Eric Goubault
In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural…
Persistent homology of partially ordered spaces
Cameron Calk, Eric Goubault, Philippe Malbos
In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces,…
A semi-abelian approach to directed homology
Eric Goubault
We develop a homology theory for directed spaces, based on the semi-abelian category of (non-unital) associative algebras. The major ingredient is a simplicial algebra constructed…
Directed topological complexity
Eric Goubault, Michael Farber, Aurélien Sagnier
It has been observed that the very important motion planning problem of robotics mathematically speaking boils down to the problem of finding a section to the path-space fibration,…
On directed homotopy equivalences and a notion of directed topological complexity
Eric Goubault
This short note introduces a notion of directed homotopy equivalence and of "directed" topological complexity (which elaborates on the notion that can be found in e.g. Farber's boo…
Covering space theory for directed topology
Eric Goubault, Emmanuel Haucourt, Sanjeevi Krishnan
The state space of a machine admits the structure of time. For example, the geometric realization of a precubical set, a generalization of an unlabeled asynchronous transition syst…