A proof of Tait's Conjecture on alternating-achiral knots

Abstract: 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 an alternating -achiral knot. Then there exists a minimal projection {\Pi} of K in S^2 \subset S^3 and an involution {\phi}:S^3\toS^3 such that: 1) {\phi} reverses the orientation of $S^3$; 2) {\phi}(S^2) = S^2; 3) {\phi} ({\Pi}) = {\Pi}; 4) {\phi} has two fixed points on {\Pi} and hence reverses the orientation of K. The purpose of this paper is to prove this statement.