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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…
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study of the notion of fibration in the setting of abstract simplicial complexes, where the concept of `homotopy' has been replaced by that of `contiguity…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…
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…