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ON SATELLITE KNOTS WITH SYMMETRIC UNION PRESENTATIONS

Tanaka, Toshifumi 大阪大学 DOI:10.18910/83207

2021.07

概要

A symmetric union in the 3-space R^3 is a knot, obtained from a knot in R^3 and its mirror image, which are symmetric with respect to a 2-plane in R^3, by taking the connected sum of them and moreover by connecting them with some vertical twists along the plane, which is a generalized operation of the connected sum of a knot and its mirror image. In this paper, we show that a satellite symmetric union with minimal twisting number one such that the order of the pattern is an odd number ≥ 3 has at least two disjoint non-parallel essential tori in the complement.

参考文献

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