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Subgroups Of The Torelli Group, Leah R. Childers
Subgroups Of The Torelli Group, Leah R. Childers
LSU Doctoral Dissertations
Let Mod(Sg) be the mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces the well-known symplectic representation:
Mod(Sg) ---> Sp(2g, Z).
The kernel of this representation is called the Torelli group, I(Sg).
We will study two subgroups of I(Sg). First we will look at the subgroup generated by all SIP-maps, SIP(Sg). We will show SIP(Sg) is not I(Sg) and is in fact an infinite index subgroup of I(Sg). We will also classify which SIP-maps are in the kernel of the Johnson homomorphism and Birman-Craggs-Johnson homomorphism.
Then we will …