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ISSN 1088-6850(e) ISSN 0002-9947(p)

The lower bound of the $\lowercase{w}$ -indices of surface links via quandle cocycle invariants

Author(s): Masahide Iwakiri
Journal: Trans. Amer. Math. Soc. 362 (2010), 1189-1210.
MSC (2000): Primary 57Q45
Posted: September 23, 2009
MathSciNet review: 2563726
Retrieve article in: PDF

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Abstract: The -index of a surface link is the minimal number of the triple points of surface braids representing . In this paper, for a given -cocycle, we consider the minimal number of the -indices of surface links whose quandle cocycle invariants associated with are non-trivial, and denote it $\omega(f)$ . In particular, we show that $\omega(\theta_3)=6$ and $\omega(\theta_p)\geq 7$ , where $\theta_n$ is Mochizuki's -cocycle of the dihedral quandle of order and is an odd prime integer $\not=3$ . As a consequence, for a given non-negative integer , there are surface knots with genus with the -index .

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