An Alexander method for infinite-type surfaces

The Alexander method is a combinatorial tool used to determine when two elements of the mapping class group are equal. We extend the Alexander method to include the case of infinite-type surfaces. Versions of the Alexander method was proven by Hern'andez–Morales–Valdez and Hern'andez–Hidber. As sample applications, we verify a relation in the mapping class group, show that the centers of many twist subgroups of the mapping class group are trivial, and provide a relatively smaller basis for the topology of the mapping class group.