Two theorems on the mapping class group of a surface

Abstract

The mapping class group of a closed surface of genus <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="greater-than-or-slanted-equals 3"> <mml:semantics> <mml:mrow> <mml:mo> ⩾ </mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">\geqslant 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is perfect. An infinite set of generators is given for the subgroup of maps that induce the identity on homology.