An Alexander method for infinite-type surfaces

Roberta Shapiro

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arXiv · 2107.06909

An Alexander method for infinite-type surfaces

Roberta Shapiro

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Abstract

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.

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Roberta Shapiro. 2021-07-14. An Alexander method for infinite-type surfaces. https://arxiv.org/abs/2107.06909

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