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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Calculus of embeddings

Author: Michael Weiss
Journal: Bull. Amer. Math. Soc. 33 (1996), 177-187
MSC (1991): Primary 57R40, 57R42
MathSciNet review: 1362629
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Abstract: Let $M$ and $N$ be smooth manifolds, where $M\subset N$ and $\dim (N)-\dim (M)\ge 3$. A disjunction lemma for embeddings proved recently by Goodwillie leads to a calculation up to extension problems of the base point component of the space of smooth embeddings of $M$ in $N$. This is mostly in terms of $\mathbf{imm}(M,N)$, the space of smooth immersions, which is well understood, and embedding spaces $\mathbf{emb}(S,N)$ for finite subsets $S$ of $M$ with few elements. The meaning of few depends on the precision desired.

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Additional Information

Michael Weiss
Affiliation: Dept. of Math., University of Notre Dame, Notre Dame, Indiana 46556
MR Author ID: 223956

Keywords: Embedding, immersion, calculus of functors
Additional Notes: Partially supported by the NSF.
Article copyright: © Copyright 1996 American Mathematical Society