The dealternating number and the alternation number of a closed 3-braid

Tetsuya Abe; Kengo Kishimoto

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arXiv · 0808.0573

The dealternating number and the alternation number of a closed 3-braid

Tetsuya Abe·Kengo Kishimoto

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Abstract

We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation number) and any braid index.

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Tetsuya Abe, Kengo Kishimoto. 2008-12-10. The dealternating number and the alternation number of a closed 3-braid. https://arxiv.org/abs/0808.0573

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