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.
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