The abelianization of a symmetric mapping class group
Masatoshi Sato
TL;DR
This paper computes the abelianization of the symmetric mapping class group for a double unbranched cover using advanced theta constants, and provides lower bounds for certain subgroups' abelianizations.
Contribution
It introduces a novel method using Riemann and Schottky theta constants to determine the abelianization of symmetric mapping class groups.
Findings
Abelianization of the symmetric mapping class group determined.
Lower bounds for abelianizations of some finite index subgroups established.
Method involving theta constants applied to mapping class groups.
Abstract
We determine the abelianization of the symmetric mapping class group of a double unbranched cover using the Riemann theta constant, Schottky theta constant, and the theta multiplier. We also give lower bounds of the abelianizations of some finite index subgroups of the mapping class group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry