The multi-region index of a knot

Sarah Goodhill; Adam M. Lowrance; Valeria Munoz Gonzales; Jessica Rattray; Amelia Zeh

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arXiv · 1909.11831

The multi-region index of a knot

Sarah Goodhill·Adam M. Lowrance·Valeria Munoz Gonzales·Jessica Rattray·Amelia Zeh

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Abstract

Using region crossing changes, we define a new invariant called the multi-region index of a knot. We prove that the multi-region index of a knot is bounded from above by twice the crossing number of the knot. In addition, we show that the minimum number of generators of the first homology of the double branched cover of $S^3$ over the knot is strictly less than the multi-region index. Our proof of this lower bound uses Goeritz matrices.

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Sarah Goodhill, Adam M. Lowrance, Valeria Munoz Gonzales, Jessica Rattray, Amelia Zeh. 2019-09-26. The multi-region index of a knot. https://arxiv.org/abs/1909.11831

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