1 citations · 1 across the 5 of their papers we have counts for
8 papers
Morse-Bott inequalities for endomorphisms
Enrique Macías-Virgós, Alejandro O. Majadas-Moure, David Mosquera-Lois +1
Let be a finite simplicial complex, let be a simplicial map and let be a discrete Morse-Bott function on satisfying for all simplice…
Morse-Bott Theory on posets and an homological Lusternik-Schnirelmann Theorem
D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera-Lois +1
We develop Morse-Bott theory on posets, generalizing both discrete Morse-Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik-Schnirelmann t…
Fundamental Theorems of Morse Theory on posets
D. Fernández-Ternero, E. Macías-Virgós, D. Mosquera Lois +2
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse t…
Simplicial fibrations
D. Fernández-Ternero, J. M. García Calcines, E. Macías-Virgós +1
We undertake a systematic study of the notion of fibration in the setting of abstract simplicial complexes, where the concept of `homotopy' has been replaced by that of `contiguity…
Discrete Topological complexity
D. Fernández-Ternero, E. Macías-Virgós, E. Minuz +1
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of co…
Strong discrete Morse theory and simplicial L-S category: A discrete version of the Lusternik-Schnirelmann Theorem
Desamparados Fernández-Ternero, Enrique Macías-Virgós, Nicholas A. Scoville +1
We prove a discrete version of the Lusternik-Schnirelmann theorem for discrete Morse functions and the recently introduced simplicial Lusternik-Schnirelmann category of a simplicia…
Simplicial Lusternik-Schnirelmann category
Desamparados Fernández-Ternero, Enrique Macías-Virgós, Erika Minuz +1
The simplicial LS-category of a finite abstract simplicial complex is a new invariant of the strong homotopy type, defined in purely combinatorial terms, that generalizes to arbitr…
Lusternik-Schnirelmann category of simplicial complexes and finite spaces
D. Fernández-Ternero, E. Macías-Virgós, J. A. Vilches
In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property…