On the homotopy type of Diff ( M n ) and connected problems

Dan Burghelea

Annales de l'institut Fourier (1973)

  • Volume: 23, Issue: 2, page 3-17
  • ISSN: 0373-0956

Abstract

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This paper reports on some results concerning:a) The homotopy type of the group of diffeomorphisms Diff ( M n ) of a differentiable compact manifold M n (with C ∞ -topology).b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo M n (with C o -topology). As a biproduct, one gets new facts about the homotopy groups of Diff ( D n , ∂ D n ) , Top n , Top n / O n and about the number of connected components of the space of topological and combinatorial pseudoisotopies.The results are contained in Section 1 and Section 2 and the geometric ideas in Section 3.

How to cite

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Burghelea, Dan. "On the homotopy type of ${\rm Diff}(M^n)$ and connected problems." Annales de l'institut Fourier 23.2 (1973): 3-17. <http://eudml.org/doc/74129>.

@article{Burghelea1973,
abstract = {This paper reports on some results concerning:a) The homotopy type of the group of diffeomorphisms $\{\rm Diff\}\,(M^n)$ of a differentiable compact manifold $M^n$ (with $C^\infty $-topology).b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo $M^n$ (with $C^o$-topology). As a biproduct, one gets new facts about the homotopy groups of $\{\rm Diff\}\, (D^n,\partial D^n),\{\rm Top\}_n$, $\{\rm Top\}_n/O_n$ and about the number of connected components of the space of topological and combinatorial pseudoisotopies.The results are contained in Section 1 and Section 2 and the geometric ideas in Section 3.},
author = {Burghelea, Dan},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {3-17},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the homotopy type of $\{\rm Diff\}(M^n)$ and connected problems},
url = {http://eudml.org/doc/74129},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Burghelea, Dan
TI - On the homotopy type of ${\rm Diff}(M^n)$ and connected problems
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 2
SP - 3
EP - 17
AB - This paper reports on some results concerning:a) The homotopy type of the group of diffeomorphisms ${\rm Diff}\,(M^n)$ of a differentiable compact manifold $M^n$ (with $C^\infty $-topology).b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo $M^n$ (with $C^o$-topology). As a biproduct, one gets new facts about the homotopy groups of ${\rm Diff}\, (D^n,\partial D^n),{\rm Top}_n$, ${\rm Top}_n/O_n$ and about the number of connected components of the space of topological and combinatorial pseudoisotopies.The results are contained in Section 1 and Section 2 and the geometric ideas in Section 3.
LA - eng
UR - http://eudml.org/doc/74129
ER -

References

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  2. [2] P. ANTONELLI, D. BURGHELEA, P. J. KAHN, The concordance homotopy groups. Lectures Notes in Math., Springer Verlag, Vol. 215. Zbl0222.57001
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  7. [7] A. HATCHER, This Issue. 
  8. [8] D. HENDERSON, Infinite dimensional manifolds are open sets of Hilbert space. Topology V. 9 (1970) 25-33. Zbl0167.51904MR40 #3581
  9. [9] R. LASHOF, The immersion approach to triangulation and smoothing. Proceedings of symposia in pure mathematics. Vol. XXII, 131-164. Zbl0236.57010MR47 #5879
  10. [10] C. MORLET, Isotopie et pseudoïsotopie. C.R. Acad. Sc., A t. 266 (1968) 559-560 and «Cours Pecot», Collège de France (1969). Zbl0174.54602MR38 #5228
  11. [11] C. ROURKE et B. SANDERSON, Δ-sets (to appear). 
  12. [12] H. TODA, p-primary components of homotopy groups IV. Memoirs of College of Science Univ. Kyoto V. XXXVII p. 297-332. Zbl0095.16802

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