### Abstract

Let M and N be smooth manifolds. The calculus of embeddings produces, for every k greater than or equal to 1, a best degree less than or equal to k polynomial approximation to the cofunctor taking an open V C M to the space of embeddings from V to N. In this paper, a description of these polynomial approximations in terms of equivariant mapping spaces is given, for k greater than or equal to 2. The description is new only for k greater than or equal to 3. In the case k = 2 we recover Haefliger's approximation and the known result that it is the best degree less than or equal to 2 approximation. (C) 2002 Published by Elsevier Science Ltd.

Original language | English |
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Pages (from-to) | 509-524 |

Number of pages | 15 |

Journal | Topology |

Volume | 42 |

DOIs | |

Publication status | Published - May 2003 |

### Keywords

- embedding
- functor calculus
- homotopy limit
- diagonal limit

## Cite this

Goodwillie, T. G., Klein, J. R., & Weiss, M. (2003). A Haefliger Style Description of the Embedding Calculus Tower.

*Topology*,*42*, 509-524. https://doi.org/10.1016/S0040-9383(01)00027-1