Unfortunately, not much to report mathematically. 4-d case is now totally solved (modulo my adviser checking it). H
Here's what I'm dealing with:
Consider an arbitrary homomorphism from S1 into S3xS3xS3xS3 = G is given by z -> (za, zb, zc, zd).
I can use this to define an action of S1 on S3xS3 via z*(p,q) = (za p z-c, zbqz-d)
Now, it's clear that the
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