On a Theorem of Burde and de Rham

Daniel S. Silver; Susan G. Williams

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arXiv · 0908.2260

On a Theorem of Burde and de Rham

Daniel S. Silver·Susan G. Williams

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Abstract

We generalize a theorem of Burde and de Rham characterizing the zeros of the Alexander polynomial. Given a representation of a knot group $π$, we define an extension of $π$, the Crowell group. For any GL(n,C) representation of $π$, the zeros of the associated twisted Alexander polynomial correspond to representations of the Crowell group into the group of dilations of C^n.

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BibTeX RIS

Daniel S. Silver, Susan G. Williams. 2009-08-16. On a Theorem of Burde and de Rham. https://arxiv.org/abs/0908.2260

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