I'm interested in groups of maps, and particularly
in the role played by the involutions in such groups.
Right now, I'm concentrating on diffeomorphisms
in one variable. Maria Roginskaya and I have worked
out some things, and we are aware of some work of
Sternberg, Mather, Smale, Robbins, Ahern and Rosay, Calica,
Kopell, Takens, Sergeraert, Young, Afraimovitch, Liu,
relating to conjugacy, normal forms, conventional
multipliers and moduli. I'd be glad to hear of sources.
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One question: does anyone study the diffeomorphism group of Euclidean spaces with anything other than the relative topology from the linear Frechet space of all smooth endomorphisms? Note that the group is not closed in this topology; one can invent others in which it is a complete TVS, but not separable. This seems like a reasonable thing to do.
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