The Alexander method is a combinatorial tool used to determine when two elements of the mapping class group are equal. In this paper we extend the Alexander method to include the case of infinite-type surfaces. Versions of the Alexander method were proven by Hernández--Morales--Valdez, Hernández--Hidber, and Dickmann. As sample applications, we verify a particular relation in the mapping class group, show that the centralizers of many twist subgroups of the mapping class group are trivial, and provide a simple basis for the topology of the mapping class group.

The author is supported by NSF grant DMS 1745583.