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Floer Homology for Knots and $\text{SU(2)}$-Representations for Knot Complements and Cyclic Branched Covers

Published online by Cambridge University Press:  20 November 2018

Olivier Collin
Olivier Collin*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC email: collin@math.ubc.ca
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Abstract

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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 ${{S}^{3}}$.

Keywords

57M5757M1257M2557M05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 2 , 01 April 2000 , pp. 293 - 305
Copyright
Copyright © Canadian Mathematical Society 2000

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