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The authors consider the Schrodinger Map equation in 2+1 dimensions, with values into Si 1/2. This admits a lowest energy steady state Q, namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space ?'. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology XC?'."