On the Jacobi group and the mapping class group of 𝑆³×𝑆³

Krylov, Nikolai

doi:10.1090/S0002-9947-02-03051-9

On the Jacobi group and the mapping class group of $S^3\times S^3$
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by Nikolai A. Krylov PDF

Trans. Amer. Math. Soc. 355 (2003), 99-117 Request permission

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 $S^3\times S^3$.

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