The Miller–Morita–Mumford classes associate to an oriented surface bundle a class . It was proved by the author, Madsen and Tillman [J. Amer. Math. Soc. 19 (2006) 759-779] that the mod reduction vanishes when is divisible by . In this note we prove that the reduction vanishes when is divisible by . We also define for each integer a characteristic class which satisfies .
"Secondary characteristic classes of surface bundles." Algebr. Geom. Topol. 9 (1) 293 - 303, 2009. https://doi.org/10.2140/agt.2009.9.293