Monotonic Simplification and Recognizing Exchange Reducibility

William W. Menasco

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Monotonic Simplification and Recognizing Exchange Reducibility

William W. Menasco

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Abstract

The Markov Theorem Without Stabilization (MTWS) (see math.GT/0310279) established the existence of a calculus of braid isotopies that can be used to move between closed braid representatives of a given oriented link type without having to increase the braid index by stabilization. Although the calculus is extensive there are three key isotopies that were identified and analyzed--destabilization, exchange moves and elementary braid preserving flypes. One of the critical open problems left in the wake of the MTWS is the "recognition problem"--determining when a given closed n-braid admits a specified move of the calculus. In this note we give an algorithmic solution to the recognition problem for three isotopies of the MTWS calculus--destabilization, exchange moves and braid preserving flypes. The algorithm is directed by a complexity measure that can be "monotonic simplified" by that application of "elementary moves".

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BibTeX RIS

William W. Menasco. 2005-07-06. Monotonic Simplification and Recognizing Exchange Reducibility. https://arxiv.org/abs/math/0507124

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