Research

My research is focused on mapping class groups and understanding their cohomology. In my PhD thesis, I studied the periodicity phenomena that occur in the mapping class group of a non-orientable surface with marked points. This phenomenon was useful to partially determine the entire cohomology of such groups in sufficiently large dimensions. My current objective is to further explore the cohomology of mapping class group of non-orientable surfaces, including surfaces of infinite type. Additionally, I am studying some models of classifying spaces of these groups.

Publications:

• A spine for the decorated Teichmüller space of a punctured non-orientable surface (arXiv)

(with Rita Jiménez Rolland, Porfirio L. León Álvarez and Luis Jorge Sanchez Saldaña)  

Preprint (2025)

• The proper geometric dimension of the mapping class group of an orientable surface with punctures  (arXiv)

(with Rita Jiménez Rolland, Porfirio L. León Álvarez and Luis Jorge Sanchez Saldaña) 

Journal of Group Theory (2025)

• Farrell cohomology of the pure mapping class group of non-orientable surfaces  (arXiv)

Preprint (2024)

• On the dimension of Harer's spine for the decorated Teichmüller space  (arXiv)

(with Rita Jiménez Rolland, Porfirio L. León Álvarez and Luis Jorge Sanchez Saldaña) 

Accepted in Homology, Homotopy and Applications (2024)

• Periodicity of the pure mapping class group of non-orientable surfaces  (arXiv)

(with Miguel A. Xicoténcatl and Rita Jiménez Rolland) 

Proceedings of the American Mathematical Society (2024)

• The Nielsen Realization Problem for Non-Orientable Surfaces (arXiv)

(with Miguel A. Xicoténcatl) 

Topology and its Applications (2024)

• El problema de realización de Nielsen para superficies no orientables

Morfismos Vol. 25 No. 1 (2021), 23-40.  

Other writings:

• Cohomología de Farrel de Grupos Modulares de Superficies no Orientables. (PhD Thesis)

• La homología de los espacios de configuraciones. (Master Thesis)