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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
-
J. L. Gross, Prime $3$-manifolds and the doubling operation, (to appear).
- H. Seifert, Topologie Dreidimensionaler Gefaserter Räume, Acta Math. 60 (1933), no. 1, 147–238 (German). MR 1555366, DOI https://doi.org/10.1007/BF02398271
- Friedhelm Waldhausen, Eine Klasse von $3$-dimensionalen Mannigfaltigkeiten. I, II, Invent. Math. 3 (1967), 308–333; ibid. 4 (1967), 87–117 (German). MR 235576, DOI https://doi.org/10.1007/BF01402956
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55.66
Retrieve articles in all journals with MSC: 55.66
Additional Information
Keywords:
Homology sphere,
torus knot,
fundamental group,
presentation,
symmetric group,
representation
Article copyright:
© Copyright 1970
American Mathematical Society