A Haefliger Style Description of the Embedding Calculus Tower

T. G. Goodwillie, J. R. Klein, Michael Weiss

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish
Pages (from-to)509-524
Number of pages15
JournalTopology
Volume42
DOIs
Publication statusPublished - May 2003

Keywords

  • embedding
  • functor calculus
  • homotopy limit
  • diagonal limit

Cite this

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

In: Topology, Vol. 42, 05.2003, p. 509-524.

Research output: Contribution to journalArticle

Goodwillie, T. G. ; Klein, J. R. ; Weiss, Michael. / A Haefliger Style Description of the Embedding Calculus Tower. In: Topology. 2003 ; Vol. 42. pp. 509-524.
@article{bfdcd4d7348c4d51ad538b4e85cebe3b,
title = "A Haefliger Style Description of the Embedding Calculus Tower",
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.",
keywords = "embedding, functor calculus, homotopy limit, diagonal limit",
author = "Goodwillie, {T. G.} and Klein, {J. R.} and Michael Weiss",
year = "2003",
month = "5",
doi = "10.1016/S0040-9383(01)00027-1",
language = "English",
volume = "42",
pages = "509--524",
journal = "Topology",
issn = "0040-9383",
publisher = "Elsevier Limited",

}

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 -