Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T15:57:14.247Z Has data issue: false hasContentIssue false
  • English
  • Français

The η-Invariants of Cusped Hyperbolic 3-Manifolds

Published online by Cambridge University Press:  20 November 2018

Robert Meyerhoff  and
Mingqing Ouyang
Robert Meyerhoff
Affiliation:
Department of Mathematics Boston College Chestnut Hill, MA USA 02167, e-mail: meyerhoff-mt@hermes.bc.edu
Mingqing Ouyang
Affiliation:
Department of Mathematics University of Michigan Ann Arbor, MI USA 48109, e-mail: mouyang@math.lsa.umich.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we define the η-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.

Keywords

Primary: 57M5053C30Secondary: 58G25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 204 - 213
Copyright
Copyright © Canadian Mathematical Society 1997

References

[1] Atiyah, M., Patodi, V. and Singer, I., Spectral asymmetry and Riemannian geometry, I,Math. Proc.Cambridge Philo. Soc. 77 (1975), 43–69.Google Scholar
[2] Meyerhoff, R., Density of the Chern-Simons invariant for hyperbolic 3-manifolds, in Low-dimensional topology and Kleinian groups, London Math. Soc. Lect. Notes 112, (ed. D. B. A. Epstein), Cambridge University Press, (1987), 217–240.Google Scholar
[3] Meyerhoff, R. and Neumann, W., An asymptotic formula for the ë-invariant of hyperbolic 3-manifolds, Comment. Math. Helvetici 67 (1992), 28–46.Google Scholar
[4] Meyerhoff, R. and Ruberman, D., Mutation and the ë-invariant, J. Differential Geom. 31 (1990), 101–130.Google Scholar
[5] Neumann, W., Combinatorics of triangulations and the Chern-Simons invariant for hyperbolic 3-manifolds. In: Topology’90, Proceedings of the Research Semester on Low Dimensional Topology, de Gruyter Verlag, 1992.Google Scholar
[6] Neumann, W. and Zagier, D., Volumes of hyperbolic 3-manifolds, Topology 24 (1985), 307–332.Google Scholar
[7] Ouyang, M., A simplicial formula for the ë-invariant of hyperbolic 3-manifolds, Topology 36 (1997), 411– 421.Google Scholar
[8] Rolfsen, D., Knots and Links, Publish or Perish, 1990.Google Scholar
[9] Thurston, W., Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982), 357–381.Google Scholar
[10] Thurston, W., The geometry and topology of 3-manifolds, Lecture Notes, Princeton Univ., 1978.Google Scholar
[11] Wall, C. T. C., Non-additivity of the signature, Invent. Math. 7 (1969), 269–274.Google Scholar
[12] Yoshida, T., The ë-invariant of hyperbolic 3-manifolds, Invent. Math. 81 (1985), 473–514.Google Scholar