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Writhe-like invariants of alternating links. (English) Zbl 1464.57001

It is known that the writhe of any reduced alternating diagram of an alternating link is an invariant as a result of the fact that any reduced alternating diagram is obtained from any other reduced alternating diagram of the same link via flypes. The authors derive several quantities from Seifert graphs of reduced alternating link diagrams. They show that these quantities are invariants when restricted to reduced alternating link diagrams and this is why they were called writhe-like invariants. These invariants are easy to calculate compared to some other invariants, especially invariants that are defined recursively.

MSC:

57K10 Knot theory
57K31 Invariants of 3-manifolds (including skein modules, character varieties)
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