The Hauptvermutung for C ∞ homeomorphisms II. A proof valid for open 4-manifolds

M. G. Scharlemann; L. C. Siebenmann

Compositio Mathematica (1974)

  • Volume: 29, Issue: 3, page 253-264
  • ISSN: 0010-437X

How to cite

top

Scharlemann, M. G., and Siebenmann, L. C.. "The Hauptvermutung for $C^\infty $ homeomorphisms II. A proof valid for open 4-manifolds." Compositio Mathematica 29.3 (1974): 253-264. <http://eudml.org/doc/89239>.

@article{Scharlemann1974,
author = {Scharlemann, M. G., Siebenmann, L. C.},
journal = {Compositio Mathematica},
language = {eng},
number = {3},
pages = {253-264},
publisher = {Noordhoff International Publishing},
title = {The Hauptvermutung for $C^\infty $ homeomorphisms II. A proof valid for open 4-manifolds},
url = {http://eudml.org/doc/89239},
volume = {29},
year = {1974},
}

TY - JOUR
AU - Scharlemann, M. G.
AU - Siebenmann, L. C.
TI - The Hauptvermutung for $C^\infty $ homeomorphisms II. A proof valid for open 4-manifolds
JO - Compositio Mathematica
PY - 1974
PB - Noordhoff International Publishing
VL - 29
IS - 3
SP - 253
EP - 264
LA - eng
UR - http://eudml.org/doc/89239
ER -

References

top
  1. [1] J. Cerf: T4 = 0.Springer Lecture Notes in Math., No. 53 (1968). Zbl0164.24502MR229250
  2. [2] M. Hirsch: On tangential equivalence of manifolds. Ann. Math.83 (1966) 211-217. Zbl0137.17704MR205265
  3. [3] M. Kervaire and J. Milnor: Groups of homotopy spheres I. Ann. of Math.77 (1963) 504-537. Zbl0115.40505MR148075
  4. [4] R.C. Kirby: Lectures on triangulation of manifolds mimeo U. of Calif., Los Angeles, 1969. 
  5. [5] R.C. Kirby and M.G. Scharlemann: A curious category which equals TOP. Proceedings of Tokyo Topology Conference of April 1973. Zbl0315.57003MR372868
  6. [6] R.C. Kirby and L.C. Siebenmann: On the triangulation of manifolds and the Hauptvermutung. Bull. Amer. Math. Soc.75 (1969) 742-749. Zbl0189.54701MR242166
  7. [7] R.C. Kirby and L.C. Siebenmann: Deformation of smooth and piecewise-linear manifold structures. Essay I of monograph (to appear). MR283807
  8. [8] R.C. Kirby and L.C. Siebenmann: Classification of sliced families of smooth or piecewise-linear manifold structures. Essay V of monograph (to appear). 
  9. [9] B. Mazur: On embeddings of spheres. Acta Mathematica105 (1961) 1-17. Zbl0096.37904MR125570
  10. [10] E. Moise: Affine structures on 3-manifolds. Ann. of Math.56 (1952) 96-114. Zbl0048.17102MR48805
  11. [11] J. Milnor: Topology from the differentiable viewpoint. Univ. Press of Virginia, Charlottesville, 1965. Zbl0136.20402MR226651
  12. [12] J.R. Munkres: Concordance of differentiable structures, two approaches. Michigan Math. J.14 (1967) 183-191. Zbl0148.17303MR212806
  13. [13] J.R. Munkres: Elementary differential topology. Ann. of Math. Study, No. 54, Princeton U. Press, 1962. Zbl0107.17201MR163320
  14. [14] C. Rourke and B.J. Sanderson: Introduction to piecewise-linear topology. Springer-Verlag, 1972. Zbl0477.57003MR350744
  15. [15] M.G. Scharlemann and L.C. Siebenmann: The Hauptvermutung for smooth singular homeomorphisms, (to appear in 1974 along with [5]). Zbl0315.57009MR372871
  16. [16] J. Shaneson: Embeddings with codimension two of spheres and h-cobordisms of S1 x S3. Bull. Amer. Math. Soc.74 (1968) 972-974. Zbl0167.21602MR230325
  17. [17] L. Siebenmann: Topological manifolds. Proc. Int. Cong. Math. Nice, 1970, Gauthier Villars, Paris, 1971. Zbl0224.57001MR423356
  18. [18] C.T.C. Wall: Bundles over a sphere. Fund. Math.61 (1967) 57-72. Zbl0312.57009MR227994

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.