New York Journal of Mathematics
Volume 27 (2021), 468-474


Nicholas G. Vlamis

Three perfect mapping class groups

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Published: March 5, 2021.
Keywords: mapping class group, infinite-type surface, automatic continuity, Cantor tree surface.
Subject: 57M07, 22F99, 20F99, 37E30, 57S05.

We prove that the mapping class group of a surface obtained from removing a Cantor set from either the 2-sphere, the plane, or the interior of the closed 2-disk has no proper countable-index normal subgroups. The proof is an application of the automatic continuity of these groups, which was established by Mann. As corollaries, we see that these groups do not contain any proper finite-index subgroups and that each of these groups has trivial abelianization.


The author recognizes support from PSC-CUNY Award #63524-00 51.

Author information

Nicholas G. Vlamis:
Department of Mathematics
CUNY Queens College
Flushing, NY 11367, USA