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Diagram Uniqueness for Highly Twisted Plats

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HTLW02 - 3-manifold workshop

Co-author: Jessica Purcell (Monash U. Melbourne Australia)

In this paper we prove that if a knot or link has a sufficiently complicated plat projection, then that plat projection is unique. More precisely, if a knot or link has a 2m-plat projection, where m is at least 3, each twist region of the plat contains at least three crossings, and n, the length of the plat, satisfies n > 4m(m − 2), then such a projection is unique up to obvious rotations. In particular, this projection gives a canonical form for such knots and links, and thus provides a classification of these links.

This talk is part of the Isaac Newton Institute Seminar Series series.

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