Algebra for Heckoid groups

Author:
Robert Riley

Journal:
Trans. Amer. Math. Soc. **334** (1992), 389-409

MSC:
Primary 57M25

MathSciNet review:
1107029

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Abstract: We introduce an infinite collection of (Laurent) polynomials associated with a -bridge knot or link normal form . Experimental evidence suggests that these "Heckoid polynomials" define the affine representation variety of certain groups, the Heckoid groups, for . We discuss relations which hold in the image of the generic representation for each polynomial. We show that, with a certain change of variable, each Heckoid polynomial divides the nonabelian representation polynomial of , where belongs to an infinite collection of -bridge knots/links determined by and the Heckoid polynomial. Finally, we introduce a "precusp polynomial" for each -bridge knot normal form, and show it is the product of two (possibly reducible) non-constant polynomials. We are preparing a sequel on the Heckoid groups and the evidence for some of the geometrical assertions stated in the introduction.

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1107029-9

Article copyright:
© Copyright 1992
American Mathematical Society