81 citations · 174 across the 12 of their papers we have counts for
6 papers · 1 filter
A directed persistent homology theory for dissimilarity functions
David Méndez, Rubén J. Sánchez-García
We develop a theory of persistent homology for directed simplicial complexes which detects persistent directed cycles in odd dimensions. We relate directed persistent homology to c…
The ring of stable homotopy classes of self-maps of -polyhedra
David Méndez
We raise the problem of realisability of rings as the ring of stable homotopy classes of self-maps of a space . By focusing on -polyhedra, we show that the dire…
Realisability problem in arrow categories
Cristina Costoya, David Méndez, Antonio Viruel
In this paper we raise the realisability problem in arrow categories. Namely, for a fixed category and for arbitrary groups , is there an object $…
The group of self-homotopy equivalences of -polyhedra
Cristina Costoya, David Méndez, Antonio Viruel
Let be a finite type -polyhedron, . In this paper we study the quotient group , where is the group of self-ho…
Homotopically rigid Sullivan algebras and Their applications
Cristina Costoya, David Méndez, Antonio Viruel
In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescrib…
Colouring simplicial complexes via the Lechuga-Murillo's model
David Méndez
L. Lechuga and A. Murillo showed that a non-oriented, simple, connected, finite graph is -colourable if and only if a certain pure Sullivan algebra associated to and …