Homology, Homotopy and Applications
Volume 15 (2013)
Manifold calculus and homotopy sheaves
Pages: 361 – 383
Manifold calculus is a form of functor calculus concerned with contravariant functors from some category of manifolds to spaces. A weakness in the original formulation is that it is not continuous in the sense that it does not handle the natural enrichments well. In this paper, we correct this by defining an enriched version of manifold calculus that essentially extends the discrete setting. Along the way, we recast the Taylor tower as a tower of homotopy sheafifications. As a spin-off we obtain a natural connection to operads: the limit of the Taylor tower is a certain (derived) space of right module maps over the framed little discs operad.
manifold calculus, functor calculus, embedding, operad, homotopy sheaf
2010 Mathematics Subject Classification
18D50, 18F10, 18G55, 57R40