On a Theorem of Burde and de Rham

Details On a Theorem of Burde and de Rham On a Theorem of Burde and de Rham

2009-08-16

arxiv.org/abs/0908.2260v1

Mathematics

Geometric Topology

9 pages, 1 figure

Scientific paper

We generalize a theorem of Burde and de Rham characterizing the zeros of the
Alexander polynomial. Given a representation of a knot group $\pi$, we define
an extension of $\pi$, the Crowell group. For any GL(n,C) representation of
$\pi$, 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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