My research lies at the intersection of algebraic topology, geometric group theory, and low-dimensional topology. I am particularly interested in understanding how algebraic, geometric, and homological properties of discrete groups interact. My work focuses on two main directions: the study of classifying spaces for families of subgroups, and the investigation of quasi-isometric invariants such as asymptotic dimension and finiteness properties. The families of groups I have studied include mapping class groups, surface braid groups, right-angled Artin groups, poly-free groups, and fundamental groups of 3-manifolds, among others.
Preprints and publications:
(with Israel Morales ). Asymptotic and cohomological dimension of surface braid groups and poly-surface groups (2025). Submitted. arXiv.
(with Nestor Colin, Luis Jorge Sánchez Saldaña and Rita Jiménez Rolland ). The proper geometric dimension of the mapping class group of an orientable surface with punctures. Journal of Group Theory (2025), https://doi.org/10.1515/jgth-2024-0227. arXiv.
(with Nestor Colin, Luis Jorge Sánchez Saldaña and Rita Jiménez Rolland ). A spine for the Teichmüller space of a punctured non-orientable surface. Bulletin of the London Mathematical Society (2025). https://doi.org/10.1112/blms.70228. arXiv.
(with Nestor Colin, Luis Jorge Sánchez Saldaña and Rita Jiménez Rolland ). On the dimension of Harer's spine for the decorated Teichmüller space (2024). To appear in Homology, Homotopy and Applications. arXiv.
(with Rita Jiménez Rolland ) On the virtually cyclic dimension of normally poly-free groups. Bol. Soc. Mat. Mex. 31, 5 (2025). https://doi.org/10.1007/s40590-024-00670-z. arXiv.
Classifying spaces for families of abelian subgroups of braid groups, RAAGs and graphs of abelian groups. Glasgow Mathematical Journal. 2024:1-18. doi:10.1017/S0017089523000496. arXiv .
(with Luis Jorge Sánchez Saldaña and Rita Jiménez Rolland ). Commensurators of abelian subgroups and the virtually abelian dimension of mapping class groups. J. Pure Appl. Algebra 228(6) (2024), 107566. arXiv.
(with Luis Jorge Sánchez Saldaña ). Classifying spaces for the family of virtually abelian subgroups of orientable 3-manifold groups. Forum Math. 34 (2022), no. 5, 1277–1296. arXiv .
In preparation:
Classifying spaces for families of abelian subgroups of surface braid groups. With Juan González-Meneses and Ramón Flores.
Balanced groups. With Jesús Hernández Hernández .
Other writings (Spanish) :
Espacios clasificantes de grupos discretos para la familia de subgrupos virtualmente abelianos . PhD thesis (2024).
El teorema de Eilenberg-Ganea para familias. Master´s thesis (2019).