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Kauffman-Harary conjecture holds for Montesinos Knots | | Marta M. Asaeda
; Jozef H. Przytycki
; Adam S. Sikora
; | | Date: |
29 May 2003 | | Subject: | Geometric Topology MSC-class: 57M25; 57M27 | math.GT | | Abstract: | The Kauffman-Harary conjecture states that for any reduced alternating diagram K of a knot with a prime determinant p, every non-trivial Fox p-coloring of K assigns different colors to its arcs. We generalize the conjecture by stating it in terms of homology of the double cover of S^3 branched along a link. In this way we extend the scope of the conjecture to all prime alternating links of arbitrary determinants. We first prove the Kauffman-Harary conjecture for pretzel knots and then we generalize our argument to show the generalized Kauffman-Harary conjecture for all Montesinos links. Finally, we speculate on the relation between the conjecture and Menasco’s work on incompressible surfaces in exteriors of alternating links. | | Source: | arXiv, math.GT/0305415 | | Services: | Forum | Review | PDF | Favorites | |
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