Learning bridge numbers of knots

arXiv:2405.05272v1 Announce Type: cross
Abstract: This paper employs various computational techniques to determine the bridge numbers of both classical and virtual knots. For classical knots, there is no ambiguity of what the bridge number means. For virtual knots, there are multiple natural definitions of bridge number, and we demonstrate that the difference can be arbitrarily far apart. We then acquired two datasets, one for classical and one for virtual knots, each comprising over one million labeled data points. With the …

abstract arxiv bridge computational cs.lg definitions difference math.gt multiple natural numbers paper type virtual