Triple Crossing Number and Double Crossing Braid Index

Daishiro Nishida

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arXiv · 1805.04428

Triple Crossing Number and Double Crossing Braid Index

Daishiro Nishida

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Abstract

Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A triple crossing is a crossing where three strands meet at a single point, such that each strand bisects the crossing. In this paper we find a relationship between the triple crossing number and the double crossing braid index, namely $\beta_2(L) \le c_3(L) + 1$. We find an infinite family of knots that achieve equality, which allows us to determine both the double crossing braid index and the triple crossing number of these knots.

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BibTeX RIS

Daishiro Nishida. 2018-05-11. Triple Crossing Number and Double Crossing Braid Index. https://arxiv.org/abs/1805.04428

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