Abstract
For the proof of Theorem 1.3 we will need to study the behavior of the bound (2.11) in the Morton-Franks-Williams inequality (we abbreviate as MFW) on positive braids. This was begun by Nakamura [Na], who settled the case MFW = 2 in the suggestive way: such braids represent only the (2, n)-torus links. (The case MFW = 1 is trivial.) We will introduce a method that considerably simplifies his proof (but still makes use of some of his ideas), and then go on to deal with MFW = 3. The example of non-sharp MFW inequality, 139365 in [HT] (the connected 2-cable of the trefoil), given in [MS], is in fact only among a small family of exceptional cases.
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Notes
- 1.
Notice we use n in a different meaning from before!
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Stoimenow, A. (2017). Positivity of 3-Braid Links. In: Properties of Closed 3-Braids and Braid Representations of Links . SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-68149-8_5
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DOI: https://doi.org/10.1007/978-3-319-68149-8_5
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