Homeomorphisms of a surface which act trivially on homology

Abstract:

Let $\mathfrak {M}$ be the mapping class group of a surface of genus $g \geqslant 3$, and $\mathcal {I}$ the subgroup of those classes acting trivially on homology. An infinite set of generators for $\mathcal {I}$, involving three conjugacy classes, was obtained by Powell. In this paper we improve Powell’s result to show that $\mathcal {I}$ is generated by a single conjugacy class and that $[\mathfrak {M},\mathcal {I}] = \mathcal {I}$.