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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On the Jacobi group and the mapping class group of $S^3\times S^3$
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by Nikolai A. Krylov
Trans. Amer. Math. Soc. 355 (2003), 99-117
DOI: https://doi.org/10.1090/S0002-9947-02-03051-9
Published electronically: September 5, 2002

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 $S^3\times S^3$.
References
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Bibliographic 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
  • Email: krylov@math.uic.edu, n.krylov@iu-bremen.de
  • Received by editor(s): July 18, 2001
  • Received by editor(s) in revised form: March 15, 2002
  • Published electronically: September 5, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 99-117
  • MSC (2000): Primary 57R50, 57R52; Secondary 20J06
  • DOI: https://doi.org/10.1090/S0002-9947-02-03051-9
  • MathSciNet review: 1928079