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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Note: For grayscale versions of this monograph, green will refer to the darker gray shaded face, orange to the lighter gray.
References
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)
Ozawa, M.: Essential state surfaces for knots and links. J. Aust. Math. Soc. 91(3), 391–404 (2011)
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
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-33302-6_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33301-9
Online ISBN: 978-3-642-33302-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)