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

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