nLab manifold calculus




Let MM be a smooth manifold without boundary and denote by 𝒪(M)\mathcal{O}(M) the poset of open subsets of MM, as defined in Wei99, ordered by inclusion. Manifold calculus is a way to study (say, the homotopy type of) contravariant functors FF from 𝒪(M)\mathcal{O}(M) to spaces which take isotopy equivalences to (weak) homotopy equivalences. In essence, it associates to such a functor a tower - called the Taylor tower - of polynomial approximations which in good cases converges to the original functor, very much like the approximation of a function by its Taylor series. (BriWei)

In BriWei the authors develop an enriched version.


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