Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57R50, 57R52, 20J06

Retrieve articles in all journals with MSC (2000): 57R50, 57R52, 20J06


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
Email: krylov@math.uic.edu, n.krylov@iu-bremen.de

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03051-9
PII: S 0002-9947(02)03051-9
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