The extension of Johnson's homomorphism from the Torelli group to the mapping class group (Q1210509)

The mapping class group \(M_ g\) of a Riemannian surface \(\Sigma_ g\) of genus \(g\geq 2\) is studied through its action on \(\pi_ 1(\Sigma_ g)\). The author represents \(M_ g\) by its action on the lower central series of \(\pi_ 1(\Sigma_ g)\) using methods of \textit{Dennis Sullivan} and \textit{D. Johnson}. The main theorems show that Johnson's homomorphism can be extended from the Torelli group to the mapping class group via a crossed homomorphism.