  The importance of the fusion relation of loops was recognized in the context
of spin structures on the loop space by Stolz and Teichner and further
developed by Waldorf. On a spin manifold M the equivalence classes of `fusive'
spin structures on the loop space LM, incorporating the fusion property, strong
regularity and reparameterization-invariance, are shown to be in 1-1
correspondence with equivalence classes of string structures on M. The
identification is through the affine space of `string' cohomology classes
considered by Redden.
