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Infinitely many two-variable generalisations of the Alexander-Conway polynomial | | David De Wit
; Atsushi Ishii
; Jon Links
; | | Date: |
21 May 2004 | | Journal: | Algebr. Geom. Topol. 5 (2005) 405-418 | | Subject: | Geometric Topology MSC-class: 57M25, 57M27, 17B37, 17B81 | math.GT | | Abstract: | We show that the Alexander-Conway polynomial Delta is obtainable via a particular one-variable reduction of each two-variable Links-Gould invariant LG^{m,1}, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of Delta. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG^{m,1} does not satisfy a second-order characteristic identity unless m=1. To demonstrate that the one-variable reduction of LG^{m,1} satisfies the defining skein relation of Delta, we evaluate the kernel of a quantum trace. | | Source: | arXiv, math.GT/0405403 | | Services: | Forum | Review | PDF | Favorites | |
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