On the fibration of augmented link complements
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We study the fibration of augmented link complements. Given the diagram of an augmented link we associate a spanning surface and a graph. We then show that this surface is a fiber for the link complement if and only if the associated graph is a tree. We further show that fibration is preserved under Dehn filling on certain components of these links. This last result is then used to prove that within a very large class of links, called locally alternating augmented links, every link is fibered.
KeywordsLink complements Fibered manifolds
Mathematics Subject Classification57M05 57M25
I am very grateful to Alan Reid for his guidance during my graduate program. I am also thankful to Cameron Gordon for helpful conversations and João Nogueira and Jessica Purcell for their comments on an early draft of this work. Finally I would like to thank the referee for his careful reading of this paper and his many comments which helped improve it.
- 1.Adams, C.: Augmented Alternating Link Complements are Hyperbolic, Low-Dimensional Topology and Kleinian Groups (Coventry-Durham, 1984), London Mathematical Society Lecture Notes Series, vol. 112, pp. 115–130. Cambridge University Press, Cambridge (1986)Google Scholar
- 3.Futer, D.: Fiber detection for state surfaces (preprint)Google Scholar
- 5.Futer, D., Kalfagianni, E., Purcell, J.: Guts of surfaces and the colored Jones polynomial. In: Monograph to appear in Lecture Notes in Mathematics, vol. 2069. Springer, BerlinGoogle Scholar
- 9.Goodman, S., Tavares, G.: Pretzel-fibered links. Bol. Soc. Bras. Mat., vol 15, no 1 e 2, pp. 85–96 (1984)Google Scholar
- 12.Melvin, P.M., Morton, H.R.: Fibred knots of genus 2 formed by plumbing Hopf bands. J. Lond. Math. Soc. 34(2), 159–168 (1986)Google Scholar
- 16.Rolfsen, D.: Knots and Links. AMS Chelsea Publishing, Providence (2003)Google Scholar
- 17.Stallings, J.: On Fibering of Certain 3-manifolds Topology of 3-manifolds and Related Topics. Prentice-Hall, Englewood Cliffs (1962)Google Scholar