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A Primer on Mapping Class Groups (PMS-49) by Dan Margalit, Benson Farb

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Chapter Six

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The Symplectic Representation and the Torelli Group

One of the fundamental aspects of Mod(Sg) is its action on H1(Sg; Z). The representation common16 : Mod(Sg) → Aut(H1(Sg; Z)) is like a first linear approximation to Mod(Sg), and we can try to transfer our knowledge of the linear group Aut(H1(Sg; )) to the group Mod(Sg).

As we show in Section 6.1, ...

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