GEOMETRY AND KINEMATICS OF 2 SKYRMIONS

In Skyrme's soliton model of baryons, a single Skyrmion has six degree s of freedom, so it is expected that two-Skyrmion dynamics at modest e nergies can be modelled by motion on a 12-dimensional space of Skyrme fields. A candidate for this space is generated by the gradient flow o f the potential energy function, descending from the unstable, baryon number two, hedgehog solutions of the Skyrme field equation. An appare ntly very similar space is obtained by restricting the gradient flow t o the Skyrme fields derived from SU(2) Yang-Mills instantons of charge two. On both of these spaces, one may quotient out by the group of tr anslations and isospin rotations. Hartshorne's geometrical description of charge two instantons leads us to a conjecture for the global stru cture of the 6-dimensional quotient space. The conjectured structure i s that of complex projective 3-space, with complex conjugate points on one projective plane identified and the real points in this plane rem oved.