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1999 Embeddings from the point of view of immersion theory : Part I
Michael Weiss
Geom. Topol. 3(1): 67-101 (1999). DOI: 10.2140/gt.1999.3.67


Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor Vemb(V,N) from the poset O of open subsets of M to spaces. We therefore abstract some of the properties of this cofunctor, and develop a suitable calculus of such cofunctors, Goodwillie style, with Taylor series and so on. The terms of the Taylor series for the cofunctor Vemb(V,N) are explicitly determined. In a sequel to this paper, we introduce the concept of an analytic cofunctor from to spaces, and show that the Taylor series of an analytic cofunctor F converges to F. Deep excision theorems due to Goodwillie and Goodwillie–Klein imply that the cofunctor Vemb(V,N) is analytic when dim(N) dim(M)3.


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Michael Weiss. "Embeddings from the point of view of immersion theory : Part I." Geom. Topol. 3 (1) 67 - 101, 1999.


Received: 10 May 1998; Revised: 5 May 1999; Accepted: 13 May 1999; Published: 1999
First available in Project Euclid: 21 December 2017

zbMATH: 0927.57027
MathSciNet: MR1694812
Digital Object Identifier: 10.2140/gt.1999.3.67

Primary: 57R40
Secondary: 57R42

Keywords: calculus of functors , ‎embedding‎ , immersion

Rights: Copyright © 1999 Mathematical Sciences Publishers

Vol.3 • No. 1 • 1999
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