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Proceedings of the American Mathematical Society

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A model for closed orientable $ 3$-manifolds of genus $ 1$

Author: J. A. Narvarte
Journal: Proc. Amer. Math. Soc. 37 (1973), 287-290
MSC: Primary 57A10; Secondary 55F55
MathSciNet review: 0309117
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Abstract: In this paper we obtain a rectangular model for each closed orientable 3-manifold of genus 1 by identifications of the unit cube via unimodular plane involutions. The desirability of the model is indicated with regard to the fibring of such manifolds by circles, together with the development of a corresponding model for the connected sum of two such manifolds.

References [Enhancements On Off] (What's this?)

  • [1] Harvey Cohn, Sphere fibration induced by uniformization of modular group, J. London Math. Soc. 43 (1968), 10–20. MR 0228435,
  • [2] H. Seifert, Topologie 3-dimensionaler gefaserter Räume, Acta Math. 60 (1932), 147-238.
  • [3] W. Threlfall and H. Seifert, Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen spharischen Räumen, Math. Ann. 107 (1932), 543-586.

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Keywords: Genus 1, rectangular model, unimodular plane involution, fibre space
Article copyright: © Copyright 1973 American Mathematical Society

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