The abelianization of the level 2 mapping class group
Masatoshi Sato
TL;DR
This paper computes the abelianization of the level 2 mapping class group and extends a homomorphism from the Torelli group to this level, advancing understanding of their algebraic structures.
Contribution
It provides the first explicit determination of the abelianization for the level 2 mapping class group and extends a key homomorphism from the Torelli group.
Findings
Abelianization of level 2 mapping class group determined
Homomorphism of Torelli group extended to level 2 group
Results contribute to the algebraic understanding of mapping class groups
Abstract
In this paper, we determine the abelianization of the level d mapping class group for d=2 and odd d. We also extend the homomorphism of the Torelli group defined by Heap to a homomorphism of the level 2 mapping class group.
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