On the Jacobi Group and the Mapping Class Group of $S^3\times S^3$

Details On the Jacobi Group and the Mapping Class Group of $S^3\times S^3$ On the Jacobi Group and the Mapping Class Group of $S^3\times S^3$

2001-07-01

arxiv.org/abs/math/0107005v1

Mathematics

Algebraic Topology

23 pages

Scientific paper

The paper containes 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 the mapping class group of $S^3\times S^3$ with generators and defining relations. We also compute cohomology of the group $\Gamma^J$ and determine a 2-cocycle that corresponds to the mapping class group of $S^3\times S^3$.

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