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- W2898393198 abstract "For a positive integer $nge 3$, the collection of $n$-sided polygons embedded in $3$-space defines the space of geometric knots. We will consider the subspace of equilateral knots, consisting of embedded $n$-sided polygons with unit length edges. Paths in this space determine isotopies of polygons, so path-components correspond to equilateral knot types. When $nle 5$, the space of equilateral knots is connected. Therefore, we examine the space of equilateral hexagons. Using techniques from symplectic geometry, we can parametrize the space of equilateral hexagons with a set of measure preserving action-angle coordinates. With this coordinate system, we provide new bounds on the knotting probability of equilateral hexagons." @default.
- W2898393198 created "2018-11-02" @default.
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- W2898393198 date "2018-10-28" @default.
- W2898393198 modified "2023-09-27" @default.
- W2898393198 title "Knotting Probability of Equilateral Hexagons." @default.
- W2898393198 hasPublicationYear "2018" @default.
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