Skip to main content
    • Aa
    • Aa

An infinite family of non-Haken hyperbolic 3-manifolds with vanishing Whitehead groups

  • Andrew J. Nicas (a1)

A manifold M is said to be aspherical if its universal covering space is contractible. Farrell and Hsiang have conjectured [3]:

Conjecture A. (Topological rigidity of aspherical manifolds.) Any homotopy equivalence f: N → M between closed aspherical manifolds is homotopic to a homeomorphism,

and its analogue in algebraic K-theory:

Conjecture B. The Whitehead groups Whj1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]S. E. Cappell . Manifolds with fundamental group a generalized free product. I. Bull. Amer. Math. Soc. 80 (1974), 11931198.

[2]S. E. Cappell . Unitary nilpotent groups and Hermitian K-theory. Bull. Amer. Math. Soc. 80 (1974), 11171122.

[4]J. Hempel . Orientation reversing involutions and the first Betti number for finite coverings of 3-manifolds. Invent. Math. 67 (1982), 133142.

[5]J. Hempel . Homology of coverings. Pacific J. Math. 112 (1984), 83113.

[8]A. J. Nicas and C. W. Stark . Higher Whitehead groups of certain bundles over Seifert manifolds. Proc. Amer. Math. Soc. 91 (1984), 15.

[13]R. G. Swan . K-theory of finite Groups and Orders. Lecture Notes in Math.149, Springer-Verlag, 1970.

[15]W. Thurston . Three dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math. Soc. 6 (1982), 357381.

[16]F. Waldhausen . Algebraic K-theory of generalized free products. Ann. of Math. 108 (1978), 135256.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *