The normal closure of a bounding pair map in its mapping class group

Abstract

Johnson showed that the normal subgroup of a mapping class group generated by the genus $1$ bounding pair maps is equal to the Torelli group. Generalizing Johnson's result, we give two descriptions of the normal subgroup generated by the genus $n$ bounding pair maps using the Chillingworth and the Casson--Morita invariants.

v2: 20 pages, 9 figures. Version 1 contained an error in Proposition 4, and this invalidated the main result. Version 2 corrects this error and contains new main results. v1: 9 pages, 2 figures