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SOLVING ORIENTED TANGLE EQUATIONS INVOLVING 4-PLATS

ISABEL K. DARCY

Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA

https://doi.org/10.1142/S0218216505004214Cited by:5 (Source: Crossref)

Abstract

The system of unoriented tangle equations and is completely solved for the tangles U and as a function of where K₁ and K₂ are 4-plats, and and rational tangles such that |f₁g₂ - g₁f₂| > 1. As an application, it is completely determined when one 4-plat can be obtained from another 4-plat via a signed crossing change.

Keywords:

AMSC: Primary 57M25, Secondary 92C40

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