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Decomposition into 3-Balls

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2069)

Abstract

In this chapter, we start with a connected link diagram and explain how to construct state graphs and state surfaces. We cut the link complement in S 3 along the state surface, and then describe how to decompose the result into a collection of topological balls whose boundaries have a checkerboard coloring.

Keywords

  • Projection Plane
  • State Circle
  • Regular Neighborhood
  • Ideal Edge
  • Combinatorial Description

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    Note: For grayscale versions of this monograph, green will refer to the darker gray shaded face, orange to the lighter gray.

References

  1. Menasco, W.W.: Polyhedra representation of link complements. In: Low-Dimensional Topology (San Francisco, CA, 1981). Contemporary Mathematics, vol. 20, pp. 305–325. American Mathematical Society, Providence (1983)

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  2. Ozawa, M.: Essential state surfaces for knots and links. J. Aust. Math. Soc. 91(3), 391–404 (2011)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Przytycki, J.H.: From Goeritz matrices to quasi-alternating links. In: The Mathematics of Knots. Contributions in Mathematical and Computational Sciences, vol. 1, pp. 257–316. Springer, Heidelberg (2011). doi:10.1007/978-3-642-15637-3_9

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Futer, D., Kalfagianni, E., Purcell, J. (2013). Decomposition into 3-Balls. In: Guts of Surfaces and the Colored Jones Polynomial. Lecture Notes in Mathematics, vol 2069. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33302-6_2

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