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

Nikolai A. Krylov
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Abstract

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 $Γ^J$ by the group of 7-dimensional homotopy spheres. Using a presentation of the group $Γ^J$ and the $μ$-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 $Γ^J$ and determine a 2-cocycle that corresponds to the mapping class group of $S^3\times S^3$.

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Nikolai A. Krylov. 2001-07-01. On the Jacobi Group and the Mapping Class Group of $S^3\times S^3$. https://arxiv.org/abs/math/0107005

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