On the Jacobi group and the mapping class group of $S^3\times S^3$
Open Access
- 5 September 2002
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 355 (1), 99-117
- https://doi.org/10.1090/s0002-9947-02-03051-9
Abstract
The paper contains a proof that the mapping class group of the manifold $S^3\times S^3$ is isomorphic to a central extension of the (full) Jacobi group $\Gamma ^J$ by the group of 7-dimensional homotopy spheres. Using a presentation of the group $\Gamma ^J$ and the $\mu$-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 $\Gamma ^J$ and determine 2-cocycles that correspond to the mapping class group of $S^3\times S^3$.