4 citations · 9 across the 12 of their papers we have counts for
14 papers
Homotopic distance and generalized motion planning
E. Macías-Virgós, D. Mosquera-Lois, M. J. Pereira-Sáez
We prove that the homotopic distance between two maps defined on a manifold is bounded above by the sum of their subspace distances on the critical submanifol of any Morse-Bott fun…
Rayleigh quotient and left eigenvalues of quaternionic matrices
E. Macías-Virgós, M. J. Pereira-Sáez, Ana D. Tarrío-Tobar
We study the Rayleigh quotient of a Hermitian matrix with quaternionic coefficients and prove its main properties. As an application, we give some relationships between left and ri…
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study of the notion of fibration in the setting of abstract simplicial complexes, where the concept of `homotopy' has been replaced by that of `contiguity…
Homotopic distance between functors
E. Macías-Virgós, D. Mosquera-Lois
We introduce a notion of categorical homotopic distance between functors by adapting the notion of homotopic distance in topological spaces, recently defined by the authors to the…