Salem-Boyd sequences and Hopf plumbing

Eriko Hironaka

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arXiv · math/0506602

Salem-Boyd sequences and Hopf plumbing

Eriko Hironaka

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Abstract

Given a fibered link, consider the characteristic polynomial of the monodromy restricted to first homology. This generalizes the notion of the Alexander polynomial of a knot. We define a construction, called iterated plumbing, to create a sequence of fibered links from a given one. The resulting sequence of characteristic polynomials has the same form as those arising in work of Salem and Boyd in their study of distributions of Salem and P-V numbers. From this we deduce information about the asymptotic behavior of the large roots of the generalized Alexander polynomials, and define a new poset structure for Salem fibered links.

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BibTeX RIS

Eriko Hironaka. 2005-06-29. Salem-Boyd sequences and Hopf plumbing. https://arxiv.org/abs/math/0506602

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