Calculus of embeddings

Weiss, Michael

doi:10.1090/S0273-0979-96-00657-X

Calculus of embeddings
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by Michael Weiss PDF

Bull. Amer. Math. Soc. 33 (1996), 177-187 Request permission

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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