Kokoro Tanaka (University of Tokyo)
Title: Braid indices of surface-knots and colorings by quandles

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Abstract:
The braid index of a surface-knot $F$ is defined to be the minimum number among the degrees of all simple surface braids whose closures are ambient isotopic to $F$. In this talk, we give a lower bound of the braid index of a surface-knot using the colorings by a quandle. As an application, we determine the braid indices of $S^2$-knots for infinitely many examples and give an infinite series of ribbon surface-knots of genus $g$ whose braid indices are $s+2$ for each pair of integers $g ¥geq 0$ and $s ¥geq 1$.