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Left orderability of cyclic branched covers of rational knots \(C(2n+1,2m,2)\). (English) Zbl 1486.57024

A sufficient condition for the left orderability of the fundamental group of the \(r\)-th cyclic branched cover of a prime knot is the existence of certain non abelian representations of the knot group in \(SL_2(\mathbb{R})\). In this paper the author study the left orderability of the fundamental groups of cyclic branched covers of the rational knots \(C(2n+1,2m,2)\) in the Conway notation by using real points on the nonabelian \(SL_2(\mathbb{C})\)-character varieties of the knot group.

MSC:

57K31 Invariants of 3-manifolds (including skein modules, character varieties)
57K32 Hyperbolic 3-manifolds
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