Mahler measure of Alexander polynomials

Details Mahler measure of Alexander polynomials Mahler measure of Alexander polynomials

2001-05-28

arxiv.org/abs/math/0105234v3

Mathematics

Geometric Topology

18 pages, 8 figures. Small revisions and corrections

Scientific paper

Let l be an oriented link of d components in a homology 3-sphere. For any nonnegative integer q, let l(q) be the link of d-1 components obtained from l by performing 1/q surgery on the dth component. Then the Mahler measure of the Alexander polynomial of l(q) converges to the Mahler measure of the Alexander polynomial of l as q goes to infinity, provided that some other component of l has nonzero linking number with the dth. Otherwise, the Mahler measure of the Alexander polynomial of l(q) has a well-defined bu different limiting behavior. Examples are given of links for which the Mahler measure of the Alexander polynomial is small. Possible connection with hyperbolic volume are discussed.

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