The abelianization of the level L mapping class group

We calculate the abelianizations of the level L subgroup of the genus g mapping class group and the level L congruence subgroup of the 2g × 2g symplectic group for L odd and g ≥ 3. Historical note. I originally wrote this paper in March of 2008. Towards the end of that month, I gave a master class on the Torelli group at the University of Aarhus. That master class ended in a conference, and I had intended to speak about this paper at that conference. However, I learned that both Bernard Perron and Masatoshi Sato had proven similar theorems and intended to speak about them at the same conference! Sato was a graduate student and had actually proved somewhat better results (in particular, he could deal with L = 2), so I decided not to publish this paper. Sato’s work appeared in [19], and Perron’s work was sketched in [14]. See my later paper [18] for results for L not divisible by 4. Dealing with the case where L is divisible by 4 is still open.