Research

Interests: Mapping class groups, geometric group theory, low-dimensional topology

Preprints 

• Cloning systems and action operads, with V. Carmona, F. Cantero Morán, J. J. Gutiérrez. Preprint 2023, 25 pages.

• Block mapping class groups and their finiteness properties, with J. Aroca, M. Cumplido, R. Skipper and X. Wu. Preprint 2022, 19 pages. 

• A note on nilpotent subgroups of automorphism groups of RAAGs (with A. Genevois). Just a short note (2016).

Papers

1. Asymptotic mapping class groups of Cantor manifolds and their finiteness properties (With K.-U. Bux, J. Flechsig, N. Petrosyan and X. Wu; with an appendix by O. Randal-Williams).  To appear in Revista Matemática Iberoamericana. 

2. Isomorphisms and commensurability of surface Houghton groups, with G. Domat and C. J. Leininger. Preprint 2023, to appear in Journal of Group Theory. 

3. Surface Houghton groups, with K.-U- Bux, H. Kim and C. J. Leininger.  Mathematische Annalen (2023).

4. El desinterés por la carrera investigadora entre el estudiantado de matemáticas en España: un análisis por sexo (in Spanish), with L. Cruz-Castro, L. Sanz-Menéndez and Ágata Timón. La Gaceta de la RSME, 26 (2023), 24 pages. 

5. Big mapping class groups and the co-Hopfian property. (With C. J. Leininger and A. McLeay.) Michigan Math. J., 74 (2), 253-281.

6. Matching arc complexes: connectedness and hyperbolicity. (With R. de Pool and A. Fernández). Expositiones Mathematicae, Volume 40, Issue 2, June 2022.

7. Asymptotic mapping class groups of closed surfaces punctured along Cantor sets, with L. Funar. Moscow Mathematical Journal 21 (2021). 

8. The first integral cohomology of big mapping class groups, with P. Patel and N. Vlamis. International Mathematics Research Notices, Volume 2020, Issue 22, November 2020, 

9. Big mapping class groups: an overview, with Nick Vlamis. To appear in In the tradition of Thurston (ed. A. Papadopoulos). 

10. Big Torelli groups: generation and commensurations. With T. Ghaswala, A. E. Kent, A. McLeay, J. Tao, R. Winarski.  Groups, Geometry, and Dynamics 13 (2019).

11. Quotients of mapping class groups by power subgroups. With L. Funar. Bulletin of the London Math. Soc. 51 (2019)

12. Representations of pure symmetric automorphism groups, with C. Martínez-Pérez, Israel Journal of Mathematics 232 (2019) 

13. Trees, homology, and automorphism groups of RAAGs, with J. L. Fernández, P. Fernández, and C. Martínez-Pérez. Journal of Algebraic Combinatorics 50 (2019)

14. Holomorphic maps between moduli spaces, with S. Antonakoudis and J. Souto. Ann. Inst. Fourier 68 (2018)

15. On the geometry of graphs associated to infinite-type surfaces, with F. Valdez. Math. Zeitschrift 289 (2018). (Note: As of June 2021, this version supersedes the published version, which has a missing hypothesis in Theorem 1.7).

16. On the virtually-cyclic dimension of mapping class groups, with D. Juan-Pineda and A. Trujillo-Negrete. Alg. Geom. Top 18 (2018).

17. Combinatorial superrigidity for graphs associated to surfaces. Topology, Geometry and Algebra of low-dimensional manifolds (RIMS Kokyuroku 1991)

18. Arc and curve graphs for infinite-type surfaces, with A. Fossas and H. Parlier. Proc. AMS 145 (2017).

19. Geometric dimension of lattices in classical simple Lie groups, with D. Degrijse, C. Martínez-Pérez and J. Souto. Journal of Topology 10 (2017).

20. Exhausting curve complexes by finite rigid sets, with C. Leininger. Pacific Journal of Mathematics 282 (2016).

21. On the first cohomology of automorphism groups of graph groups, with C. Martínez-Pérez. Journal of Algebra 452 (2016).

22. Injective maps between flip graphs, with T. Koberda and H. Parlier. Ann. Inst. Fourier 65 (2015).

23. Hyperbolic structures on surfaces and geodesic currents, with C. J. Leininger. In Algorithmic and Geometric Topics Around Free Groups and Automorphisms, with V. Diekert, C. Leininger, P. Silva, A. Weiss. Advanced Courses in Math (CRM), Birkhauser.

24. The proper geometric dimension of the mapping class group, with C. Martínez-Pérez. Alg. Geom. Top 14 (2014).

25. A remark on homomorphisms from right-angled Artin groups to mapping class groups, with J. Souto. C. R. Acad. Sci. Paris 351 (2013).

26. Rigidity phenomena in mapping class groups, with J. Souto. In Handbook of Teichmüller Theory VI.

27. Finite rigid sets in curve complexes, with C. Leininger. Journal of Topology and Analysis 5 (2013).

28. Convexity of strata in diagonal pants of surfaces, with C. Lecuire, H. Parlier and K. J. Shackleton. Publicacions Matemàtiques 57 (2013).

29. Hyperbolic structures on surfaces. In Geometry, Topology and Dynamics of Character Varieties, World Scientific 23 (2012). See companion notes by Chris Leininger.

30. Homomorphisms between mapping class groups, with J. Souto. Geometry and Topology 16 (2012).

31. Automorphisms of the graph of free splittings, with J. Souto. Michigan Math Journal 60 (2011).

32. Simplicial embeddings between pants graphs. Geom. Dedicata 144 (2010)

33. Injections of mapping class groups, with C. Leininger and J. Souto. Geometry and Topology 13 (2009).

34. A characterisation of quasiconformal maps using triangles, with P. Haïssinsky. Publicacions Matemàtiques 52 (2008).

35. Constructing convex planes in the pants complex, with H. Parlier and K. J. Shackleton. Proc. AMS 137 (2009).

36. Totally geodesic subgraphs of the pants complex, with H. Parlier and K. J. Shackleton. Math. Res. Lett. 15 (2008).

37. An obstruction to the strong relative hyperbolicity of a group, with J. W. Anderson and K. J. Shackleton. Journal of Group Theory 10 (2007).

38. Uniformly exponential growth and mapping class groups of surfaces, with J. W. Anderson and K. J. Shackleton. In the Tradition of Ahlfors-Bers IV Contemp. Math. 432, Amer. Math. Soc.

39. Free subgroups of mapping class groups, with J. W. Anderson and K. J. Shackleton. Conformal Geometry and Dynamics 11 (2007). ( Corrigendum in Conformal Geometry and Dynamics 13 (2009))

40. The Weil-Petersson geometry of the five-times punctured sphere. In Spaces othe f Kleinian groups LMS Lecture Notes 329.

Book

• Algorithmic and Geometric Topics Around Free Groups and Automorphisms, with V. Diekert, C. Leininger, P. Silva, A. Weiss. Advanced Courses in Math (CRM), Birkhauser.