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Diagrams Without Non-prime Arcs

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

Abstract

In this chapter, which is independent from the remaining chapters, we will restrict ourselves to A-adequate diagrams D(K) for which the polyhedral decomposition includes no non-prime arcs or switches. In this case, one can simplify the statement of Theorem 5.14 and give an easier combinatorial estimate for the guts of M A . This is done in Theorem 7.2, whose proof takes up the bulk of the chapter.

Keywords

  • Cell Complex
  • Diagrammatic Statement
  • Hyperbolic Geometry
  • Sample Application
  • State Circle

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Fig. 7.1
Fig. 7.2
Fig. 7.3

Notes

  1. 1.

    Note: For grayscale versions of this monograph, orange faces in the figures will appear light gray, and green ones will appear darker gray.

References

  1. Lickorish, W.B.R., Thistlethwaite, M.B.: Some links with nontrivial polynomials and their crossing-numbers. Comment. Math. Helv. 63(4), 527–539 (1988)

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© 2013 Springer-Verlag Berlin Heidelberg

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Futer, D., Kalfagianni, E., Purcell, J. (2013). Diagrams Without Non-prime Arcs. 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_7

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