Skip to main content

A survey of diffeomorphism groups

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 428))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. P. L. Antonelli, D. Burghelea, P. J. Kahn, The concordance homotopy groups of geometric automorphism groups, Springer lecture notes #215.

    Google Scholar 

  2. _____, Gromoll groups, Diff (S n) and bilinear constructions of exotic spheres, Bull. Am. Math. Soc. 76 (1970), 722–727.

    MathSciNet  Google Scholar 

  3. _____, The non-finite homotopy type of some diffeomorphism groups, Topology 11 (1972), 1–49.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. K. Agoston, On handle decompositions and diffeomorphisms, Trans. Am. Math. Soc. 137 (1969), 21–36.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Arkowitz, C. Curjel, The group of homotopy equivalences of a space, Bull. Am. Math. Soc. 70 (1964), 293–296.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Asada, Contraction of the group of diffeomorphisms of IR n, Proc. Japan Acad. 41 (1965), 273–276.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. S. Birman, D. R. J. Chillingsworth, On the homeotopy group of a non-orientable surface, Proc. Camb. Philos. Soc. 71 (1972), 437–448.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. S. Birman, H. Hilden, Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group, Bull. Am. Math. Soc. (6) 78 (1972), 1002–1004.

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Browder, Diffeomorphisms of 1-connected manifolds, Trans. Am. Math. Soc. 128 (1967), 155–163.

    MathSciNet  MATH  Google Scholar 

  10. W. Browder, T. Petrie, Diffeomorphisms of manifolds and semifree actions on homotopy spheres, Bull. Am. Math. Soc. 77 (1971), 160–163.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Brown, Constructing isotopies in non-compact 3-manifolds, Bull. Am. Math. Soc. (3) 78 (1972), 461–464.

    Article  MATH  Google Scholar 

  12. D. Burghelea, R. Lashoff, The homotopy type of the space of diffeomorphisms, Part I, preprint.

    Google Scholar 

  13. J. Cerf, Groupes d'automorphismes et groupes de difféomorphismes des variétés compactes de dimension 3. Bull. Soc. Math. France 87 (1959), 319–329.

    MathSciNet  MATH  Google Scholar 

  14. _____, Groupes d'homotopie locaux et groupes d'homotopie mixtes des espaces bitopologiques. Presque n-locale connexion. Applications. C. R. Acad. Sci. Paris 253 (1961), 363–365.

    MathSciNet  MATH  Google Scholar 

  15. _____, Isotopie et pseudo-isotopie, Proc. Int. Cong. Math. Moscow (1966), 429–437.

    Google Scholar 

  16. _____, La nullité de π0 (Diff S 3). Theorems de fibration des espaces de plongements. Applications. Séminaire Henri Cartan, 1962/63, Exp. 8, 13 pp. Secrétariat mathématiques, Paris, 1964: 1) Position du problem, Exp. 9–10, 27 pp.: 2) Espaces fonctionnels liés aux decomposition d'une sphere plongée dans IR 3 Exp. 20, 29 pp. 3) Construction d'une section pour le revêtement. Exp. 21, 25 pp.

    Google Scholar 

  17. _____, The pseudo-isotopy theorem for simply connected differentiable manifolds, Manifolds-Amsterdam 1970 Springer lecture notes #197, p. 76–82.

    Google Scholar 

  18. _____, La stratification naturelle des espaces de fonctions différentiables réeles et le théorèm de la pseudoisotopie. Haut Études Sci. Publ. Math. No. 39 (1970) 5–173.

    Google Scholar 

  19. _____, Topologie de certains espaces de plongements, Bull. Soc. Math. France 89 (1971), 227–380.

    MathSciNet  MATH  Google Scholar 

  20. A. Chenciner, Pseudo-isotopies différentiables and pseudoisotopies linéaires par morceaux. C. R. Acad. Sci. Paris Sér. A–B 270 (1970), A1312–A1315.

    MathSciNet  MATH  Google Scholar 

  21. A. Chenciner, F. Laudenbach, Contribution à une théorie de Smale à un paramètre dan le cas non-simplement connexe, Ann. Sci. Ècole Norm. Sup. (4) 3 (1970), 109–478.

    MathSciNet  MATH  Google Scholar 

  22. J. A. Childress, Restricting isotopies of spheres, Pac. J. of Math. (2) 45 (1973).

    Google Scholar 

  23. D. R. J. Chillingsworth, A finite set of generators for the homeotopy groups of a non-orientable surface, Proc. Camb. Philos. Soc. 65 (1969), 409–430.

    Article  Google Scholar 

  24. C. J. Earl, J. Eells, The diffeomorphism group of a compact Riemann Surface, Bull. Am. Math. Soc. 73 (1967) 557–559.

    Article  MathSciNet  MATH  Google Scholar 

  25. D. G. Ebin, J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. (2) 92 (1970), 102–163.

    Article  MathSciNet  MATH  Google Scholar 

  26. D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165–173.

    MathSciNet  MATH  Google Scholar 

  27. R. Geoghegan, Manifolds of piecewise linear maps and a related normed linear space, Bull. Am. Math. Soc. 77 (1971), 629–632.

    Article  MathSciNet  MATH  Google Scholar 

  28. _____, On spaces of homeomorphisms embeddings and functions I, Topology 11 (1972), 159–177.

    Article  MathSciNet  MATH  Google Scholar 

  29. H. Gluck, Embeddings and automorphisms of open manifolds, Topology of Manifolds (Proc. Inst. Univ. Georgia, Athens, Georgia 1969), 394–406.

    Google Scholar 

  30. _____, Restriction of isotopies, Bull. Am. Math. Soc. 69 (1963), 78–82.

    Article  MathSciNet  MATH  Google Scholar 

  31. M. E. Hamstrom, Homotopy groups of the space of homeomorphisms of a 2-manifold, Illinois J. of Math. 10 (1966), 563–573.

    MathSciNet  MATH  Google Scholar 

  32. A. Hatcher, A K2 obstruction for pseudo-isotopies, Ph.D. thesis, Stanford 1971.

    Google Scholar 

  33. _____, The second obstruction for pseudo-isotopies, Bull. Am. Math. Soc. (6) 78 (1972), 1005–1008.

    Article  MathSciNet  MATH  Google Scholar 

  34. D. W. Henderson, R. Schori, Topological classification of infinite dimensional manifolds by homotopy type, Bull. Amer. Math. Soc. (1) 76 (1970), 121–124.

    Article  MathSciNet  MATH  Google Scholar 

  35. J. P. E. Hodgson, Automorphisms of meta-stably connected PL-manifolds, Proc. Camb. Philos. Soc. 69 (1971), 75–77.

    Article  MathSciNet  MATH  Google Scholar 

  36. _____, Automorphisms of thickenings, Bull. Am. Math. Soc. 73 (1967), 678–681.

    Article  MathSciNet  MATH  Google Scholar 

  37. _____, A generalization of "Concordance of PL homeomorphisms of S p × S q", Can. J. Math. (3) 24 (1972), 426–431.

    Article  MathSciNet  MATH  Google Scholar 

  38. _____, Poincaré complex thickenings and concordance obstructions, Bull. Am. Math. Soc. 76 (1970), 1039–1043.

    Article  MathSciNet  MATH  Google Scholar 

  39. _____, Obstructions to concordance for thickenings, Invent. Math. 5 (1968), 292–316.

    Article  MathSciNet  MATH  Google Scholar 

  40. W. C. Hsiang, W. Y. Hsiang, On compact subgroups of the diffeomorphism groups of Kervaire spheres, Ann. of Math. (2) 85 (1967), 359–368.

    Article  MathSciNet  MATH  Google Scholar 

  41. J. R. Hubbeck, On homotopy commutative H-spaces, Topology 8 (1969), 119–126.

    Article  MathSciNet  Google Scholar 

  42. J. F. P. Hudson, Concordance and isotopy of PL embeddings, Bull. Am. Math. Soc. 72 (1966), 534–535.

    Article  MathSciNet  MATH  Google Scholar 

  43. _____, Concordance, isotopy and diffeotopy, Ann. of Math. (2) 91 (1970), 425–448.

    Article  MathSciNet  MATH  Google Scholar 

  44. _____, Piecewise linear embeddings and isotopies, Bull. Ann. Math. Soc. 72 (1966), 536–537.

    Article  MathSciNet  MATH  Google Scholar 

  45. J. F. P. Hudson, W. B. R. Lickorish, Extending piecewise linear concordances, Quart. J. of Math., Oxford Ser (2) 22 (1971), 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  46. L. S. Husch, Homotopy groups of PL embedding spaces, Pac. J. Math. 33 (1970), 149–155.

    Article  MathSciNet  MATH  Google Scholar 

  47. _____, Local algebraic invariants for Δ-sets, Rocky Mountain J. Math. (2) 2 (1972), 289–298.

    Article  MathSciNet  MATH  Google Scholar 

  48. L. S. Husch, T. B. Rushing, Restriction of isotopies and concordances, Mich. Math. J. 16 (1969), 303–307.

    Article  MathSciNet  MATH  Google Scholar 

  49. D. W. Kahn, A note on H-equivalences, Pac. J. of Math. (1) 42 (1972), 77–80.

    Article  MathSciNet  MATH  Google Scholar 

  50. _____, The group of stable self equivalences, Topology 11 (1972), 133–140.

    Article  MathSciNet  MATH  Google Scholar 

  51. P. J. Kahn, Self equivalences of (n-1) connected 2n manifolds, Math. Ann. 180 (1969), 26–47.

    Article  MathSciNet  MATH  Google Scholar 

  52. M. Kato, A concordance classification of PL homeomorphisms of S P × s q, Topology 8 (1969), 371–383.

    Article  MathSciNet  MATH  Google Scholar 

  53. M. Kervaire, J. Milnor, Groups of homotopy spheres I, Ann. of Math. 2 (1963), 504–537.

    Article  MathSciNet  MATH  Google Scholar 

  54. W. A. LaBach, On diffeomorphisms of the n-disc, Proc. Japan Acad. 43 (1967), 448–450.

    Article  MathSciNet  MATH  Google Scholar 

  55. T. C. Lawson, Some examples of non-finite diffeomorphism groups, Proc. Am. Math. Soc. (2) 34 (1972), 570–572.

    Article  MATH  Google Scholar 

  56. J. A. Leslie, On a differential structure for the group of diffeomorphisms, Topology 6 (1967), 263–271.

    Article  MathSciNet  MATH  Google Scholar 

  57. J. Levine, Inertia groups of manifolds and diffeomorphisms of spheres, Amer. J. Math. 92 (1970), 243–258.

    Article  MathSciNet  MATH  Google Scholar 

  58. _____, Self equivalences of S n × S k, Trans. Am. Math. Soc. 143 (1969), 523–543.

    Google Scholar 

  59. J. Mather, The vanishing of the homology of certain groups of homeomorphisms, Topology 10 (1971), 297–298.

    Article  MathSciNet  MATH  Google Scholar 

  60. C. Morlet, Lissage des homéomorphisms, CR Acad. Sci. Paris Sér. A-B 268 (1969), A1323–1326.

    MathSciNet  Google Scholar 

  61. S. P. Novikov, Differentiable sphere bundles (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 71–96.

    MathSciNet  Google Scholar 

  62. _____, Homotopy properties of the group of diffeomorphisms of the sphere (Russian), Dokl. Akad. Nauk. SSSR 148 (1963), 32–35: (English) Doklady 4 (part 1) (1963), 27–31.

    MathSciNet  MATH  Google Scholar 

  63. P. Olum, Self equivalences of pseudo-projective planes II. Simple equivalences. Topology 10 (1971), 257–260.

    Article  MathSciNet  MATH  Google Scholar 

  64. H. Omori, Local structures on groups of diffeomorphisms, J. Math. Soc. Japan 24 (1972), 60–88.

    Article  MathSciNet  MATH  Google Scholar 

  65. _____, On the group of diffeomorphisms of a compact manifold, Global Analysis (Proc. Sympos. Pure Math. Vol. XV, Berkeley 1968), AMS 1970.

    Google Scholar 

  66. R. Palais, Local triviality of the restriction map for embeddings, Comment. Math. Helv. 34 (1960), 305–312.

    Article  MathSciNet  MATH  Google Scholar 

  67. _____, Homotopy theory of infinite dimensional manifolds, Topology 5 (1966), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  68. S. Robertson, Retracting diffeomorphisms of spheres, Proc. Am. Math. Soc. 24 (1970), 57–59.

    MathSciNet  MATH  Google Scholar 

  69. H. Sato, Diffeomorphism groups and classification of manifolds, J. Math. Soc. Japan 21 (1969), 1–36.

    Article  MathSciNet  MATH  Google Scholar 

  70. _____, Diffeomorphism groups of S p × S q and exotic spheres, Quart. J. Math. Oxford (Ser. 2) 20 (1969), 255–276.

    Article  MathSciNet  MATH  Google Scholar 

  71. B. Schellenberg, The group of homotopy self equivalences of some compact CW complexes, Math. Ann. 200 (1973), 253–266.

    Article  MathSciNet  MATH  Google Scholar 

  72. R. Schultz, Composition constructions on diffeomorphisms of S p × S q, Pac. J. Math. (3) 42 (1972), 739–754.

    Article  MATH  Google Scholar 

  73. G. P. Scott, The space of homeomorphisms of a 2-manifold, Topology 9 (1970), 97–109.

    Article  MathSciNet  MATH  Google Scholar 

  74. W. Shih, On the group ζ[x] of homotopy equivalence maps, Bull. Am. Math. Soc. 70 (1964), 361–365.

    Article  MathSciNet  MATH  Google Scholar 

  75. M. Shub and D. Sullivan, Homology and dynamical systems, preprint.

    Google Scholar 

  76. L. Siebenmann, Notices Am. Math. Soc. (1967), p. 852 and p. 942.

    Google Scholar 

  77. A. J. Sieradski, Stabilization of self equivalences of the pseudo-projective spaces, Mich. Math. J. (2) 19 (1972), 109–119.

    Article  MathSciNet  MATH  Google Scholar 

  78. _____, Twisted self homotopy equivalences, Pac. J. Math. 34 (1970), 789–802.

    Article  MathSciNet  MATH  Google Scholar 

  79. S. Smale, Diffeomorphisms of the 2-sphere, Proc. Am. Math. Soc. 10 (1969), 621–626.

    MathSciNet  MATH  Google Scholar 

  80. T. E. Stewart, On groups of diffeomorphisms, Proc. Am. Math. Soc. 11 (1970), 559–563.

    Article  MathSciNet  MATH  Google Scholar 

  81. A. G. Swarup, Pseudo-isotopies of S 3 × S 1, Math. Z. 121 (1971), 201–205.

    Article  MathSciNet  Google Scholar 

  82. R. Tindell, Relative concordance, Topology of manifolds (Proc. Inst., Univ. of Georgia, Athens, Georgia, 1969), 453–457.

    Google Scholar 

  83. E. C. Turner, Diffeomorphisms homotopic to the identity, Trans. Am. Math. Soc. (2) 188 (1974), 1–10.

    MATH  Google Scholar 

  84. _____, Diffeomorphisms of a product of spheres, Invent. Math. 8 (1969), 69–82.

    Article  MathSciNet  MATH  Google Scholar 

  85. _____, Nilpotent diffeomorphism groups, preprint.

    Google Scholar 

  86. _____, Rotational symmetry: basic properties and application to knot manifolds, Invent. Math. 19 (1973), 219–234.

    Article  MathSciNet  MATH  Google Scholar 

  87. _____, Some finite diffeomorphism groups, Illinois J. Math, to appear.

    Google Scholar 

  88. J. B. Wagoner, Algebraic invariants for pseudo-isotopies, Proc. Liverpool Sing. Sympos. II, Springer lecture notes #209, 1971.

    Google Scholar 

  89. R. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56–88.

    Article  MathSciNet  MATH  Google Scholar 

  90. C. T. C. Wall, Classification problems in differential topology, IV: Diffeomorphisms of handlebodies, Topology 2 (1963), 263–272.

    Article  MathSciNet  MATH  Google Scholar 

  91. _____, Diffeomorphisms of 4-manifolds, J. London Math. Soc. 39 (1964), 131–140.

    Article  MathSciNet  MATH  Google Scholar 

  92. K. Wang, Free S 1 actions and the group of diffeomorphisms, preprint, to appear, Trans. Am. Math. Soc.

    Google Scholar 

  93. R. Wells, Concordance of diffeomorphisms and the pasting construction, Duke Math. J. (4) 39 (1972), 665–693.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Louis F. McAuley

Rights and permissions

Reprints and permissions

Copyright information

© 1974 Springer-Verlag

About this paper

Cite this paper

Turner, E.C. (1974). A survey of diffeomorphism groups. In: McAuley, L.F. (eds) Algebraic and Geometrical Methods in Topology. Lecture Notes in Mathematics, vol 428. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070539

Download citation

  • DOI: https://doi.org/10.1007/BFb0070539

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07019-1

  • Online ISBN: 978-3-540-37300-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics