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arXiv · 1703.02258

The mapping class group orbits in the framings of compact surfaces

Nariya Kawazumi
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Abstract

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. In addition, we discuss how this invariant behaves in the relative case, which Randal-Williams studied for $g > 1$.

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Nariya Kawazumi. 2017-03-07. The mapping class group orbits in the framings of compact surfaces. https://arxiv.org/abs/1703.02258

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