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A prime curve is determined by its $VF$-matrix


Author: Louis Zulli
Journal: Proc. Amer. Math. Soc. 130 (2002), 2165-2172
MSC (2000): Primary 57M15; Secondary 05C50
DOI: https://doi.org/10.1090/S0002-9939-01-06320-1
Published electronically: December 27, 2001
MathSciNet review: 1896054
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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  • [4] L. Zulli, A matrix invariant of curves in $S^2$, to appear in J. Knot Theory Ramifications.

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Additional Information

Louis Zulli
Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
Email: zullil@lafayette.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06320-1
Keywords: Vertex-face matrix, prime curve, Gauss code
Received by editor(s): August 14, 2000
Received by editor(s) in revised form: February 1, 2001
Published electronically: December 27, 2001
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society

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