Commentarii Mathematici Helvetici


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Volume 77, Issue 1, 2002, pp. 125–132
DOI: 10.1007/s00014-002-8333-3

Relations among the lowest degree of the Jones polynomial and geometric invariants for a closed positive braid

TAKASHI KAWAMURA[1]

(1) GRADUATE SCHOOL OF MATHEMATICAL SCIENCES, UNIVERSITY OF TOKYO, 3-8-1 KOMABA MEGURO-KU, 153-8914 MZ, TOKYO, JAPAN

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.

Keywords: Unknotting number, four-dimensional clasp number, slice Euler characteristic, Jones polynomial

KAWAMURA TAKASHI: Relations among the lowest degree of the Jones polynomial and geometric invariants for a closed positive braid. Comment. Math. Helv. 77 (2002), 125-132. doi: 10.1007/s00014-002-8333-3