### 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 |
---|---|

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

*Topology*,

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

**A Haefliger Style Description of the Embedding Calculus Tower.** / Goodwillie, T. G.; Klein, J. R.; Weiss, Michael.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - A Haefliger Style Description of the Embedding Calculus Tower

AU - Goodwillie, T. G.

AU - Klein, J. R.

AU - Weiss, Michael

PY - 2003/5

Y1 - 2003/5

N2 - 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.

AB - 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.

KW - embedding

KW - functor calculus

KW - homotopy limit

KW - diagonal limit

U2 - 10.1016/S0040-9383(01)00027-1

DO - 10.1016/S0040-9383(01)00027-1

M3 - Article

VL - 42

SP - 509

EP - 524

JO - Topology

JF - Topology

SN - 0040-9383

ER -