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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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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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Additional Information
  • Michael Weiss
  • Affiliation: Dept. of Math., University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 223956
  • Email: weiss.13@nd.edu
  • Additional Notes: Partially supported by the NSF.
  • © Copyright 1996 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 33 (1996), 177-187
  • MSC (1991): Primary 57R40, 57R42
  • DOI: https://doi.org/10.1090/S0273-0979-96-00657-X
  • MathSciNet review: 1362629