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A prime curve is determined by its -matrix

Author(s): Louis Zulli
Journal: Proc. Amer. Math. Soc. 130 (2002), 2165-2172.
MSC (2000): Primary 57M15; Secondary 05C50
Posted: December 27, 2001
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Abstract: We show that a prime generic immersion $S^1\to S^2$ is determined up to ambient isotopy by its vertex-face matrix, and give an algorithm for obtaining the curve's Gauss code directly from that matrix.

References:

[1]: C. Dowker and M. Thistlethwaite, Classification of knot projections, Topology Appl. 16 (1983), pp. 19-31. MR 85e:57003
[2]: L. Kauffman, Gauss codes, quantum groups and ribbon Hopf algebras, Rev. Math. Phys. 5 (1993), pp. 735-773. MR 94k:57013
[3]: L. Kauffman, Virtual knot theory, European J. Combin. 20 (1999), pp. 663-690. MR 2000i:57011
[4]: L. Zulli, A matrix invariant of curves in , to appear in J. Knot Theory Ramifications.


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