The mapping class group orbits in the framings of compact surfaces

2017/03/07 by Kawazumi, Nariya
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1703.02258

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.

Related

• Groupoid-theoretical methods in the mapping class groups of surfaces
• Mapping class group orbit closures for non-orientable surfaces
• Weakly framed surface configurations, Heisenberg homology and Mapping Class Group action
• Generating the mapping class group by torsion elements of small order
• Torsion Elements in the Mapping Class Group of a Surface