By means of a result due to Fiedler, we obtain a relation between the lowest degree of the Jones polynomial and the unknotting number for any link which has a closed positive braid diagram. Furthermore, we obtain relations between the lowest degree and the slice euler characteristic or the four-dimensional clasp number.
Cite this article
Takashi Kawamura, Relations among the lowest degree of the Jones polynomial and geometric invariants for a closed positive braid. Comment. Math. Helv. 77 (2002), no. 1, pp. 125–132DOI 10.1007/S00014-002-8333-3