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# The $\eta$-invariants of cusped hyperbolic $3$-manifolds

Published:1997-06-01
Printed: Jun 1997
• Robert Meyerhoff
• Mingqing Ouyang
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## Abstract

In this paper, we define the $\eta$-invariant for a cusped hyperbolic $3$-manifold and discuss some of its applications. Such an invariant detects the chirality of a hyperbolic knot or link and can be used to distinguish many links with homeomorphic complements.
 MSC Classifications: 57M50 - Geometric structures on low-dimensional manifolds 53C30 - Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 58G25 - unknown classification 58G25