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Montesinos Links

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

Abstract

In this chapter, we study state surfaces of Montesinos links, and calculate their guts. Our main result is Theorem 8.6. In that theorem, we show that for every sufficiently complicated Montesinos link K, either K or its mirror image admits an A-adequate diagram D such that the quantity \(\vert \vert {E}_{c}\vert \vert \) of Definition 5.9 vanishes.

Keywords

  • Continue Fraction Expansion
  • Reidemeister Move
  • Horizontal Band
  • Compression Disk
  • Complex Disk

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Fig. 8.1
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Fig. 8.7
Fig. 8.9
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Fig. 8.12
Fig. 8.13

Notes

  1. 1.

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

References

  1. Burde, G., Zieschang, H.: Knots. de Gruyter Studies in Mathematics, vol. 5, 2nd edn. Walter de Gruyter, Berlin (2003)

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  2. Lackenby, M.: The volume of hyperbolic alternating link complements. Proc. Lond. Math. Soc. (3) 88(1), 204–224 (2004). With an appendix by Ian Agol and Dylan Thurston

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  3. 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). Montesinos Links. 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_8

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