13 papers
Non-unimodular transversely homogeneous foliations
E. Macías-Virgós, P. L. Martín-Méndez
We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we pr…
Non-linear Morse-Bott functions on quaternionic Stiefel manifolds
Enrique Macías-Virgós, María José Pereira-Sáez, Daniel Tanré
In the Stiefel manifold , we replace Frankel linear height function by a quadratic one. We prove this is still a Morse-Bott function, whose structure of critical levels pr…
Relative singular value decomposition and applications to LS-category
E. Macías-Virgós, M. J. Pereira-Sáez, Daniel Tanré
Let be the symplectic group of quaternionic -matrices. For any , an element of can be decomposed in $A= \begin{bmatrix} α&T\cr β&P \…
Euler calculus on spaces homeomorphic to definable sets and some applications
E. Macías-Virgós, D. Mosquera-Lois
We show that integration with respect to the Euler-Poincaré characteristic can be extended from the setting of definable sets to the setting of topological spaces homeomorphic to d…
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…