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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isospectrality and $3$-manifold groups


Author: Daniel Ruberman
Journal: Proc. Amer. Math. Soc. 129 (2001), 2467-2471
MSC (2000): Primary 57M10, 58J28
Published electronically: December 7, 2000
MathSciNet review: 1823933
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Abstract:

The Chern-Simons and $\eta$-invariants are closely related invariants of a Riemannian $3$-manifold. A difference in their behavior under taking a finite covering space is exploited to give an obstruction to a group being the fundamental group of a closed $3$-dimensional manifold.


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Additional Information

Daniel Ruberman
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02454
Email: ruberman@brandeis.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05820-2
PII: S 0002-9939(00)05820-2
Received by editor(s): March 16, 1998
Received by editor(s) in revised form: December 6, 1999
Published electronically: December 7, 2000
Additional Notes: The author was partially supported by NSF Grant 4-50645
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society