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Sorry, I meant $\Sigma^{\infty}_{+}Maps(X,A)$ of course
I think the mapping space is/must be regarded as being pointed already, so that $\Sigma^\infty Maps(X,A)$ is correct.
Abstractly, the stable splitting is the Goodwillie derivative of the functor $Maps(X,-)$, and that is a functor from and to pointed topological spaces.
added pointer to
added now detailed definitions and statements up to Snaith 74 theorem 1.1 and Boedigheimer 87, Examples 2 and 5.
So far, this material is duplicated also at configuration space of points. I think that’s okay. Once the discussion here enters the generalization as in Arone 99, the two entries will diverge.
There are diffeomorphic-invariant results on stable splitting here if needed:
Thanks! I’ll have a look.
I have now added a section (here) indicating how the stable splitting of mapping spaces is the limiting Goodwillie-Taylor tower of the mapping space functor.
I am just following the basic observations about excisiveness of the stages in the splitting formula, from the second page of Arone 99, but regarding assumptions on the space that we are homming out, and the notation and conventions on the mapping space, I am sticking with what I already had in the entry. (See the tables there for matching notation to the literature.)
$Comp=Conf$ in #11?
Yes, thanks, fixed.
added pointer to
and cross-linked with nonabelian Poincaré duality
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