Embeddings from the point of view of immersion theory : Part II

Let $M$ and $N$ be smooth manifolds. For an open $V \subset M$ let $emb (V, N)$ be the space of embeddings from $V$ to $N$ . By the results of Goodwillie and Goodwillie–Klein, the cofunctor $V \mapsto emb (V, N)$ is analytic if $dim (N) - dim (M) \geq 3$ . We deduce that its Taylor series converges to it. For details about the Taylor series, see Part I

Keywords

Embedding, immersion, calculus of functors

Mathematical Subject Classification

Primary: 57R40

Secondary: 57R42

References

Forward citations

Publication

Received: 10 May 1998

Revised: 5 May 1999

Accepted: 13 May 1999

Published: 28 May 1999

Proposed: Ralph Cohen

Seconded: Haynes Miller, Gunnar Carlsson

Authors

Thomas G Goodwillie
Department of Mathematics Brown University Box 1917 Providence Rhode Island 02912-0001 USA

Michael Weiss
Department of Mathematics University of Aberdeen Aberdeen AB24 3UE United Kingdom

Volume 3, issue 1 (1999)

Thomas G Goodwillie and Michael Weiss