Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel-Jacobi map

TL;DR

This paper revises the main results on the stable cohomology of the mapping class group with symplectic coefficients and discusses the universal Abel-Jacobi map, providing corrected proofs and additional insights.

Contribution

It offers corrected proofs of the stable cohomology results and introduces new discussion on the universal Abel-Jacobi map.

Findings

Corrected the main theorem and proof regarding stable cohomology.

Added new section on the universal Abel-Jacobi map.

Enhanced understanding of the mapping class group's cohomology with symplectic coefficients.

Abstract

This replacement corrects statement and proof of the main result. Also, a section on the universal Abel-Jacobi map has been added.