Invariants of fibred knots from moduli
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abstract

An invariant $\mu_{\alpha}(K)$ of fibred knots $K$ in a homology sphere is
defined for each $\alpha \in {\bold S}{\bold U}_n$ as follows. Since the knot
is fibred, the knot complement is described by an element of the mapping class
group, which induces an action on the variety of ${\bold S}{\bold U}_n$
representations of the surface group. Restricting attention to those
representations with holonomy along the longitude conjugate to $a \in {\bold
S}{\bold U}_n,$ one can define $\mu_{\alpha}(K)$ to be the Lefschetz number of
this action. The dependence of $\mu_\alpha(K)$ on $\alpha$ is studied and
formulas relating $\mu_{\alpha}(K)$ to $\mu_{\beta}(K)$ are derived for
$\alpha,\beta \in
${\bold S}{\bold U}_n$.$