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Sep 3, 2021 at 9:35 comment added Urs Schreiber I just found this old discussion while wondering if anyone had considered this generalization of the original question: Are nearby crossed homomorphisms out of a compact Lie group crossed-conjugate to each other?
Mar 8, 2013 at 16:47 comment added Tom Goodwillie That is the worrisome part, isn't it? But I believe that the error should just give more second-order terms.
Mar 8, 2013 at 15:24 comment added Charles Rezk I'm worried about averaging $h(x)=h(x)^y*h(y)$ over $x$. In the local coordinates, $x\mapsto x^y$ isn't linear, and a non-linear transformation might not play well with the integral.
Mar 8, 2013 at 2:16 history answered Tom Goodwillie CC BY-SA 3.0