Research
Specialist in Topology, with a focus on Algebraic Topology, Foliations, Morse Theory, and Lie Groups.
Research interests / Líneas de Investigación
- Foliation theory
- Lie groups and homogeneous spaces
- Infinite-dimensional manifolds
- Diffeological spaces
- Lusternik-Schnirelmann category
- Morse theory
- Quaternionic linear algebra
- Finite spaces and simplicial complexes
- Topological complexity
Research Papers (since 2011)
In compliance with the Spanish Law of Science, Technology and Innovation (Law 14/2011, modified by Law 17/2022), all publicly funded research articles must be made available in open access repositories. This includes the obligation to deposit the final accepted version of the research articles, along with a persistent identifier such as a DOI.
- Categorical Join and Generating Families in Diffeological Spaces (2023) - MDPI Mathematics (with Reihaneh Mehrabi) [DOI]
- Mayer-Vietoris sequence for generating families in diffeological spaces (2023) - Indag. Math. New Ser. (with R. Mehrabi) [DOI]
- $m$-Homotopic Distance (2023) - Topology Appl. (with D. Mosquera-Lois, J. Oprea) [DOI]
- Poincaré Duality for Posets (2023) - Topology Appl. (with D. Mosquera-Lois, J.A. Vilches) [DOI]
- Rayleigh quotient and left eigenvalues of quaternionic matrices (2022) - Linear and Multilinear Algebra (with M.J. Pereira-Sáez, A.D. Tarrío) [DOI]
- Fundamental theorems of Morse Theory on posets (2022) - AIMS Mathematics (with D. Fernández-Ternero, D. Mosquera-Lois, N.A. Scoville, J.A. Vilches) [DOI]
- Homotopic distance and generalized motion planning (2022) - Mediterranean Journal of Mathematics (with D. Mosquera-Lois, M.J. Pereira-Sáez) [DOI]
- Homotopic distance between maps (2022) - Math. Proc. Cambridge Philos. Soc. (with D. Mosquera-Lois) [DOI]
- Morse-Bott theory on posets and a homological Lusternik-Schnirelmann theorem (2021) - Journal of Topology and Analysis (with D. Fernández-Ternero, D. Mosquera-Lois, J.A. Vilches) [DOI]
- Simplicial fibrations (2021) - Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM (with D. Fernández-Ternero, J.M. García-Calcines, J.A. Vilches) [DOI]
- Homotopic distance between functors (2020) - Journal of Homotopy and Related Structures (with D. Mosquera-Lois) [DOI]
- Non-linear Morse-Bott functions on quaternionic Stiefel manifolds (2020) - Indag. Mathematicae New series (with M.J. Pereira-Sáez, D. Tanré) [DOI]
- Non-unimodular transversely homogeneous foliations (2021) - Ann. Inst. Fourier Grenoble (with P.L. Martín) [DOI]
- Strong discrete Morse theory and simplicial LS-category: A discrete version of the Lusternik-Schnirelmann Theorem (2020) - Discrete and Computational Geometry (with D. Fernández-Ternero, N. Scoville, J.A. Vilches) [DOI]
- Relative Singular Value Decomposition and applications to LS-category (2019) - Linear Algebra Appl. (with M.J. Pereira-Sáez, D. Tanré) [DOI]
- On the quaternionic quadratic equation $xax + bx + xc + d = 0$ (2019) - Advances in Applied Clifford Algebras (with M.J. Pereira-Sáez) [DOI]
- Simplicial Lusternik-Schnirelmann category (2019) - Publicacions Matemàtiques (with D. Fernández-Ternero, E. Minuz, J.A. Vilches) [DOI]
- Cayley Transform on Stiefel manifolds (2018) - Journal of Geometry and Physics (with M.J. Pereira-Sáez, D. Tanré) [DOI]
- Discrete topological complexity (2018) - Proceedings Amer. Math. Soc. (with D. Fernández-Ternero, E. Minuz, J.A. Vilches) [DOI]
- The Cayley transform on Lie groups, symmetric spaces and Stiefel manifolds (2018) - Revue Roumaine de Mathématiques Pures et Appliquées DOI not available
- Height functions on quaternionic Stiefel manifolds (2017) - Journal of the Ramanujan Mathematical Society (with J. Oprea, J. Strom, D. Tanré) DOI not available
- Lusternik-Schnirelmann category of simplicial complexes and finite spaces (2015) - Topology and its Appl. (with D. Fernández-Ternero, J.A. Vilches) [DOI]
- Cayley-Hamilton theorem for left eigenvalues of 3x3 quaternionic matrices (2014) - Special Matrices (with M. J. Pereira-Sáez) [DOI]
- A topological approach to left eigenvalues of quaternionic matrices (2014) - Linear and Multilinear Algebra (with M. J. Pereira-Sáez) [DOI]
- An upper bound for the Lusternik-Schnirelmann category of the symplectic group (2013) - Math. Proceedings Cambridge Phil. Soc. (with M. J. Pereira-Sáez) [DOI]
- A cohomological lower bound for the transverse LS category of a foliated manifold (2011) - Illinois J. Math (with E. Macias-Virgós) [DOI]
- De Rham cohomology of diffeological spaces and foliations (2011) - Indagationes Mathematicae (with G. Hector, E. Sanmartín) [DOI]
- Diffeomorphism group of Lie foliations (2011) - Annales Inst. Fourier Grenoble (with G. Hector, A. Sotelo-Armesto) [DOI]
- Trace map Cayley transform and the LS category of Lie groups (2011) - Annals of Global Analysis and Geometry (with A. Gómez Tato, M. J. Pereira-Sáez) [DOI]