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- W2022141293 abstract "By the works of Gusarov [2] and Habiro [3], it is known that a local move called the C n move is strongly related to Vassiliev invariants of order less than n. The coefficient of the z n term in the Conway polynomial is known to be a Vassiliev invariant of order n. In this note, we will consider to what degree the relationship is strong with respect to Conway polynomial. Let K be a knot, and K C n the set of knots obtained from a knot K by a single C n move. Let [Formula: see text] be the set of the Conway polynomials [Formula: see text] for a set of knots [Formula: see text]. Our main result is the following: There exists a pair of knots K 1 , K 2 such that ∇K 1 = ∇K 2 and [Formula: see text]. In other words, the C n Gordian complex is not homogeneous with respect to Conway polynomial." @default.
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- W2022141293 date "2006-11-01" @default.
- W2022141293 modified "2023-10-10" @default.
- W2022141293 title "LOCAL MOVES AND GORDIAN COMPLEXES" @default.
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