On the Jacobi group and the mapping class group of $S^3\times S^3$

Abstract

The paper contains a proof that the mapping class group of the manifold S 3 x S 3 is isomorphic to a central extension of the (full) Jacobi group Γ J by the group of 7-dimensional homotopy spheres. Using a presentation of the group Γ J and the p-invariant of the homotopy spheres, we give a presentation of this mapping class group with generators and defining relations. We also compute the cohomology of the group Γ J and determine 2-cocycles that correspond to the mapping class group of S 3 × S 3 .