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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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

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