Research

My research area is geometric topology. Some of my interests include low-dimensional topology; manifolds, fiber bundles, and characteristic classes; group actions and Nielsen realization; mapping class groups, diffeomorphism groups, and arithmetic groups.

Collaborators: Alina al Beaini, Mauricio Bustamante, Lei Chen, Jeffrey Giansiracusa, Junzhi Huang, Manuel Krannich, Alexander Kupers, Jean-Francois Lafont, Kathryn Mann, Nick Salter, Daniel Studenmund, Genevieve Walsh

Research articles

Note: frequently the version on this page is more up-to-date than the version on the arXiv.

Homotopy-Anosov Z^2 actions on exotic tori

with M. Bustamante arXiv:2408.09346

Surface mapping class group actions on 3-manifolds

with A. al Beaini and L. Chen Submitted. arxiv:2311.15508

Mapping class groups of exotic tori and actions by SL(d,Z)

with M. Bustamante, M. Krannich, A. Kupers Trans. Amer. Math. Soc., to appear

Mapping class groups of circle bundles over a surface

with L. Chen Michigan Math J., to appear

Symmetries of exotic negatively curved manifolds

with M. Bustamante J. Diff. Geom. 120 (2022) 2, 231-250.

Counting flat cycles in the homology of locally symmetric manifolds

with D. Studenmund arxiv: 2206.11986

Nielsen realization for sphere twists of 3-manifolds

with L. Chen Israel J. Math., to appear

Convex-cocompact subgroups of the Goeritz group

Trans. Amer. Math. Soc. 377 (2024), no. 1, 271–322.

Symmetries of exotic aspherical space forms

with M. Bustamante Submitted. arXiv:2109.09196

Finite rigid sets and the separating curve complex

with J. Huang Topology Appl. 312 (2022).

Arithmeticity of groups Z^n rtimes Z

Indiana Univ. Math. J. 71 (2022) 4, 1797-1818.

Geometric cycles and characteristic classes of manifold bundles

with appendix by M. Krannich Comment. Math. Helv. 96 (2021) 1, 1-45.

Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem

with J. Giansiracusa and A. Kupers Tunis. J. Math. 3 (2021) 1, 75-92.

Arithmeticity of the monodromy of some Kodaira fibrations

with N. Salter Compositio Math. 156 (2020) 1, 114-157.

Groups with 2-sphere Bowditch boundary

with G. Walsh Groups Geom. Dyn. 14 (2020) 3, 791-811.

Borel’s stable range for the cohomology of arithmetic groups

J. Lie Theory. 29(2019) 4, 1093-1102.

Hyperbolic groups with boundary an n-dimensional Sierpinski space

with J. Lafont J. Topol. Anal. 11 (2019) 1, 233–247.

Characteristic classes of fiberwise branched covers via arithmetic groups

Michigan Math. J. 67 (2018), 31–58.

On the non-realizability of braid groups by diffeomorphisms

with N. Salter Bull. Lond. Math. Soc., 48 (2016) 3, 457–471.

Pontryagin classes of locally symmetric manifolds

Algebr. Geom. Topol. 15 (2015) 5, 2709-2756.

Cohomological obstructions to Nielsen realization

J. Topol. 8 (2015) 2, 352–376.

Other articles

Advice from our advisor: Benson Farb

coordinating editor AMS Notices, Nov 2021.

Surface bundles in topology, algebraic geometry, and group theory

with N. Salter AMS Notices, Feb. 2020.

Realization problems for diffeomorphism groups

with K. Mann Proc. Sympos. Pure Math. 102 (2019) 131-156.

Notes

Local coefficients and Poincare duality pdf