The mapping class group orbits in the framings of compact surfaces

Nariya Kawazumi

Published 2017-03-07Version 1

We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments on the Arf invariant, while we need an extra invariant for the genus $1$ case.