Tokyo Journal of Mathematics

The Number of Vogel Operations to Deform a Link Diagram to a Closed Braid

Chuichiro HAYASHI and Hiroko SAEKI

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Vogel showed that any oriented link diagram $D$ can be deformed to a closed braid by a finite sequence of Reidemeister II moves, each performed on two coherently oriented edges in a face of $D$ such that the edges are contained in distinct Seifert circles. We show that the number of such moves is constant for a given oriented link diagram, and does not depend on the sequence of moves. An easy way of calculating the number is given.

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Tokyo J. Math., Volume 28, Number 2 (2005), 299-307.

First available in Project Euclid: 5 June 2009

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HAYASHI, Chuichiro; SAEKI, Hiroko. The Number of Vogel Operations to Deform a Link Diagram to a Closed Braid. Tokyo J. Math. 28 (2005), no. 2, 299--307. doi:10.3836/tjm/1244208192.

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