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A proof of Tait’s Conjecture on prime alternating - achiral knots

Nicola ErmottiCam Van Quach HonglerClaude Weber — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait’s Conjecture on alternating - achiral knots: Let K be a prime alternating - achiral knot. Then there exists a minimal projection Π of K in S 2 S 3 and an involution ϕ : S 3 S 3 such that: 1) ϕ reverses the orientation of S 3 ; 2) ϕ ( S 2 ) = S 2 ; 3) ϕ ( Π ) = Π ; 4) ϕ has two fixed points on Π and hence reverses...

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