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Understanding Vogel’s Algorithm for Links vs. Closed Braids

Vogel’s Algorithm explores the relationship between links and closed braids by defining key concepts such as smoothing, Serfeit circles, and defect faces. The algorithm shows how bending reduces the height of a diagram, leading to the discovery of defect faces and eventually achieving a link with compatible concentric circles. The process provides insights into closed braids as consistent orientation and cylindrical shapes. References to Kassel-Turaev's work on braid groups and an introduction to knots and braids using Seifert circles are included.

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Understanding Vogel’s Algorithm for Links vs. Closed Braids

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