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Ideal Polyhedra

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

Abstract

Recall that \({M}_{A} = {S}^{3}\setminus \setminus {S}_{A}\) is S 3 cut along the surface S A . In the last chapter, starting with a link diagram D(K), we obtained a prime decomposition of M A into 3-balls. One of our goals in this chapter is to show that, if D(K) is A-adequate (see Definition 1.1 on p. 4), each of these balls is a checkerboard colored ideal polyhedron with 4-valent vertices.

Keywords

  • Directed Edge
  • Directed Spine
  • State Circle
  • Prime Decomposition
  • Link Diagram

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Fig. 3.1
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Futer, D., Kalfagianni, E., Purcell, J. (2013). Ideal Polyhedra. 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_3

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