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Bulletin of the American Mathematical Society
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 $ {\text{\bf imm}}(M,N)$, the space of smooth immersions, which is well understood, and embedding spaces $ \text{\bf 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
Email: weiss.13@nd.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-96-00657-X
PII: S 0273-0979(96)00657-X
Keywords: Embedding, immersion, calculus of functors
Additional Notes: Partially supported by the NSF.
Article copyright: © Copyright 1996 American Mathematical Society