Research

I am interested in low-dimensional and geometric topology. My dissertation work was on trisections of smooth 4-manifolds, which involves splitting a 4-dimensional topological space into three simple pieces. Some trisection diagrams that I generated for my dissertation work are displayed below. To construct such a diagram for a flat surface bundle over a surface, I use a map from the fundamental group of the base to the mapping class group of the fiber; this map describes how the fiber transforms as each loop in the base is traversed.

As an undergraduate, I participated in an REU at San Diego State University during Summer 2012, under the supervision of Dr. Vadim Ponomarenko. This led to the following publication:

• Crawford, L., Ponomarenko, V., Steinberg, J., Williams, M. Accepted Elasticity in Local Arithmetic Congruence Monoids, Results in Mathematics 66 (2014), pp 227-245.