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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Homomorphisms of knot groups on finite groups

Author: Robert Riley
Journal: Math. Comp. 25 (1971), 603-619
MSC: Primary 55A25
MathSciNet review: 0295332
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Abstract: We describe trial and error computer programs for finding certain homomorphisms of a knot group on a special projective group $ LF(2,p),p$ prime, and programs to evaluate $ {H_1}(\mathfrak{M};{\text{Z}})$ where $ \mathfrak{M}$ is a finitely sheeted branched covering space of $ {S^3}$ associated with such a homomorphism. These programs have been applied to several collections of examples, in particular to the Kinoshita-Terasaka knots, and we state numerous conjectures based on these experiments.

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Keywords: Homomorphisms of knot groups on finite groups, homology of covering spaces
Article copyright: © Copyright 1971 American Mathematical Society