کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4658537 | 1633103 | 2014 | 11 صفحه PDF | دانلود رایگان |
We study the Morton–Franks–Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is an orthonormal basis for the inner product of the Hecke algebra of the braid group defined by Kálmán, who first obtained this result by using an interesting connection with Contact Topology.We also introduce a new technique to study the Homflypt polynomial for closures of positive braids, namely resolution trees whose leaves are simple braids. In terms of these simple resolution trees, we characterize closed positive braids for which the Morton–Franks–Williams inequality is strict. In particular, we determine explicitly the positive braid words on three strands whose closures have braid index three.
Journal: Topology and its Applications - Volume 174, 1 September 2014, Pages 14–24