Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T13:58:58.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Topologically rigid non-Haken 3-manifolds

Part of: Topological manifolds

Published online by Cambridge University Press:  09 April 2009

J. Hass  and
W. Menasco
J. Hass
Affiliation:
University of California, Davis, California, U.S.A., e-mail: [email protected]
W. Menasco
Affiliation:
SUNY at Buffalo, Buffalo, New York, U.S.A., e-mail: [email protected]
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.

A closed irreducible 3-manifold M is topologically rigid if any homotopy equivalent irreducible 3-manifold is homeomorphic to M. A construction is given which produces infinitely many non-Haken topologically rigid 3-manifolds

MSC classification

Secondary: 57N10: Topology of general $3$-manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 1 , August 1993 , pp. 60 - 71
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Aitchison, I. R., Lumsden, E. and Rubinstein, J. H., ‘Cusp structure of alternating links’, Invent. Math., to appear.Google Scholar
[2]Aitchison, I. R. and Rubinstein, J. H., ‘An introduction to polyhedral metrics of non-positive curvature on 3-manifolds’, preprint.Google Scholar
[3]Bleiler, S. and Hodgson, C., ‘Spherical space forms and Dehn surgery’, preprint.Google Scholar
[4]Gromov, M. and Thurston, W., ‘Pinching constants for hyperbolic manifolds’, Invent. Math. 89 (1987), 1–12.CrossRefGoogle Scholar
[5]Hass, J. and Scott, P., ‘Homotopy equivalence and homeomorphism of 3-manifolds’, Topology 31 (1992), 493–517.CrossRefGoogle Scholar
[6]Hatcher, A. E., ‘On the boundary curves of incompressible surfaces’, Pacific J. Math. 99 (1982), 373–377.CrossRefGoogle Scholar
[7]Menasco, W., ‘Polyhedral representation of link complements’, Contemp. Math. 20 (1983), 305–325.CrossRefGoogle Scholar
[8]Menasco, W., ‘Closed incompressible surfaces in alternating knot and link complements’, Topology 23 (1984), 37–44.CrossRefGoogle Scholar
[9]Menasco, W., ‘Determining incompressibility of surfaces in alternating knot and link complements’, Pacific J. Math. 117 (1985), 353–370.CrossRefGoogle Scholar
[10]Mostow, G. D., ‘Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms’, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53–104.CrossRefGoogle Scholar
[11]Scott, P., ‘There are no fake Seifert fiber spaces’, Ann. of Math. 117 (1983), 35–70.CrossRefGoogle Scholar
[12]Thurston, W., The geometry and topology of 3-manifolds (Lecture notes, Princeton University, 1978).Google Scholar
[13]Waldhausen, F., ‘On irreducible 3-manifolds which are sufficiently large’, Ann. of Math. 87 (1968), 56–88.CrossRefGoogle Scholar