Publications

My research lies at the intersection of algebraic topology, geometric group theory, and geometry. In particular, I am interested in studying classifying spaces for families for discrete groups, investigating their Bredon cohomology, and applications. The classifying spaces for families have many applications, to name a few: they appear in the Farrell-Jones and Baum-Connes isomorphism conjectures, can be used to define Adamson's relative cohomology, and to calculate topological complexity.

Preprints and publications:

• (with  Rita Jiménez Rolland )  On the virtually cyclic dimension of normally poly-free groups. Submitted (2023).  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 .

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).