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Floer Homology for Knots and $\SU(2)$-Representations for Knot Complements and Cyclic Branched Covers |
Canad. J. Math. 52(2000), 293-305
Published:2000-04-01
Printed: Apr 2000
Printed: Apr 2000
- Olivier Collin
Abstract
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 $\SU(2)$-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 $\SU(2)$-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
$\SU(2)$-representations of the fundamental group of cyclic
branched covers. We illustrate the method with some examples of
knots in $S^3$.
| MSC Classifications: |
57R57 - Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX] 57M12 - Special coverings, e.g. branched 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M05 - Fundamental group, presentations, free differential calculus |