Geometry & Topology

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

Thomas G Goodwillie and Michael Weiss

Full-text: Open access

Abstract

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

Article information

Source
Geom. Topol., Volume 3, Number 1 (1999), 103-118.

Dates
Received: 10 May 1998
Revised: 5 May 1999
Accepted: 13 May 1999
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883140

Digital Object Identifier
doi:10.2140/gt.1999.3.103

Mathematical Reviews number (MathSciNet)
MR1694808

Zentralblatt MATH identifier
0927.57028

Subjects
Primary: 57R40: Embeddings
Secondary: 57R42: Immersions

Keywords
Embedding immersion calculus of functors

Citation

Goodwillie, Thomas G; Weiss, Michael. Embeddings from the point of view of immersion theory : Part II. Geom. Topol. 3 (1999), no. 1, 103--118. doi:10.2140/gt.1999.3.103. https://projecteuclid.org/euclid.gt/1513883140


Export citation

References

  • R Bott, On invariants of manifolds Modern methods in complex analysis, Ann. of Math. Stud. 137, Princeton Univ. Press, Princeton, NJ (1995)29–39
  • J–P Dax, Etude homotopique des espaces de plongements, Ann. Scient. de l'Ecole Norm. Sup. 5 ( 197)2 303–377
  • T G Goodwillie, Calculus II: Analytic Functors, K–Theory, 5 (1991)/1992 295–332
  • T G Goodwillie, A multiple disjunction lemma for smooth concordance embeddings, Amer. Math. Soc. Memoirs, 86 no. 431 (1990)
  • T G Goodwillie, Excision estimates for spaces of homotopy equivalences, preprint, Brown University (1995)
  • T G Goodwillie, Excision estimates for spaces of smooth embeddings, preprint, Brown University 1998
  • T G Goodwillie, J Klein, Excision estimates for spaces of Poincaré embeddings, in preparation
  • A Haefliger, Plongements différentiables dans le domaine stable, Commentarii Math. Helv. 37 (1962)/63 155–167
  • A Haefliger, M Hirsch, Immersions in the stable range, Ann. of Math. 75 (1962) 231–241
  • M Kontsevich, Feynman Diagrams and Low–dimensional Topology, from: “Proceedings of First European Congress of Mathematics (1992), vol. II”, Birkhäuser, 97–121
  • J Milnor, On the construction FK, Algebraic Topology–-a student's guide, by J F Adams, London Math. Soc. Lecture Note Series no. 4, Cambridge University Press (1972)
  • V A Vassiliev, Cohomology of knot spaces Theory of singularities and its applications, (V I Arnold, editor), Advances in Soviet Mathematics (AMS) 1 (1990) 23–69
  • V A Vassiliev, Complements to discriminants of smooth maps: Topology and Applications, Amer. Math. Soc. Press (1992)
  • M Weiss, Calculus of embeddings, Bull. Amer. Math. Soc. 33 (1996) 177–187
  • M Weiss, Embeddings from the point of view of immersion theory, Part I, Geometry and Topology, 3 (1999) 67–101
  • G W Whitehead, Elements of Homotopy theory, Graduate texts in Mathematics, Springer (1978)