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Involutions and isotopies of lens spaces

  • Craig Hodgson
  • J. H. Rubinstein
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1144)

Abstract

In this paper we study the topology of the three-dimensional lens spaces by regarding them as two-fold branched coverings. The main result obtained is a classification of the smooth involutions on lens spaces having one-dimensional fixed point sets. We show that each such involution is conjugate, by a diffeomorphism isotopic to the identity, to an isometry of the lens space (given the standard spherical metric).

Using this classification of involutions, we deduce that genus one Heegaard splittings of lens spaces are unique up to isotopy. We apply this result to give a new proof of the classification of lens spaces up to diffeomorphism. We also compute the group of isotopy classes of diffeomorphisms of each lens space.

Keywords

Homology Class Orbit Space Morse Function Lens Space Isotopy Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Craig Hodgson
    • 1
  • J. H. Rubinstein
    • 2
  1. 1.Princeton UniversityPrincetonUSA
  2. 2.University of MelbourneParkvilleAustralia

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