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An infinite class of irreducible homology $ 3$-spheres


Author: Jonathan L. Gross
Journal: Proc. Amer. Math. Soc. 25 (1970), 173-176
MSC: Primary 55.66
DOI: https://doi.org/10.1090/S0002-9939-1970-0268895-3
MathSciNet review: 0268895
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Abstract: A class of irreducible homology $ 3$-spheres is obtained by pasting together complements of torus knots. Representations of the fundamental groups of these homology $ 3$-spheres into symmetric groups are then used to distinguish the members of an infinite subclass.


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

  • [1] J. L. Gross, Prime $ 3$-manifolds and the doubling operation, (to appear).
  • [2] H. Seifert, Topologie dreidimensionaler gefaserter Räume, Acta Math. 60 (1932), 147-238. MR 1555366
  • [3] F. Waldhausen, Eine Klasse von $ 3$-dimensionalen Mannigfaltigkeiten. II, Invent. Math. 4 (1967), 87-117. MR 0235576 (38:3880)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0268895-3
Keywords: Homology sphere, torus knot, fundamental group, presentation, symmetric group, representation
Article copyright: © Copyright 1970 American Mathematical Society

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