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

Author: Nikolai A. Krylov
Journal: Trans. Amer. Math. Soc. 355 (2003), 99-117
MSC (2000): Primary 57R50, 57R52; Secondary 20J06
Published electronically: September 5, 2002
MathSciNet review: 1928079
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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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Additional Information

Nikolai A. Krylov
Affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607
Address at time of publication: School of Engineering and Science, International University Bremen, P. O. Box 750 561, 28725 Bremen, Germany

Received by editor(s): July 18, 2001
Received by editor(s) in revised form: March 15, 2002
Published electronically: September 5, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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