New York Journal of Mathematics
Volume 28 (2022), 1137-1151


Roberta Shapiro

An Alexander method for infinite-type surfaces

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Published: August 5, 2022.
Keywords: mapping class group, Alexander method, surface topology.
Subject [2010]: 57K20.

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.

Author information

Roberta Shapiro:
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30313, USA