Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

Manifold calculus and homotopy sheaves

Pages: 361 – 383

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a20


Pedro Boavida de Brito (Mathematisches Institut, Universität Münster, Germany)

Michael Weiss (Mathematisches Institut, Universität Münster, Germany)


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

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Published 4 December 2014