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Floer Homology for Knots and
$\text{SU(2)}$-Representations for Knot Complements and Cyclic Branched Covers
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- Journal:
- Canadian Journal of Mathematics / Volume 52 / Issue 2 / 01 April 2000
- Published online by Cambridge University Press:
- 20 November 2018, pp. 293-305
- Print publication:
- 01 April 2000
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- Article
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In this article, using 3-orbifolds singular along a knot with underlying space a homology sphere
${{Y}^{3}}$, the question of existence of non-trivial and non-abelian $\text{SU(2)}$-representations of the fundamental group of cyclic branched covers of ${{Y}^{3}}$ along a knot is studied. We first use Floer Homology for knots to derive an existence result of non-abelian $\text{SU(2)}$-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian $\text{SU(2)}$-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in 
${{S}^{3}}$.
