Structure of the group of homeomorphisms preserving a good measure on a compact manifold

A. Fathi

Annales scientifiques de l'École Normale Supérieure (1980)

  • Volume: 13, Issue: 1, page 45-93
  • ISSN: 0012-9593

How to cite

top

Fathi, A.. "Structure of the group of homeomorphisms preserving a good measure on a compact manifold." Annales scientifiques de l'École Normale Supérieure 13.1 (1980): 45-93. <http://eudml.org/doc/82046>.

@article{Fathi1980,
author = {Fathi, A.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {local contractibility of the group of measure-preserving homeomorphisms; compact connected manifold without boundary; abelianization of the group of measure preserving homeomorphisms},
language = {eng},
number = {1},
pages = {45-93},
publisher = {Elsevier},
title = {Structure of the group of homeomorphisms preserving a good measure on a compact manifold},
url = {http://eudml.org/doc/82046},
volume = {13},
year = {1980},
}

TY - JOUR
AU - Fathi, A.
TI - Structure of the group of homeomorphisms preserving a good measure on a compact manifold
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1980
PB - Elsevier
VL - 13
IS - 1
SP - 45
EP - 93
LA - eng
KW - local contractibility of the group of measure-preserving homeomorphisms; compact connected manifold without boundary; abelianization of the group of measure preserving homeomorphisms
UR - http://eudml.org/doc/82046
ER -

References

top
  1. [An] R. D. ANDERSON, On Homeomorphisms as Products of Conjugates of a given Homeomorphism and its Inverse, Topology of 3-Manifolds and Related Topics, M. K. FORT, Ed., Prentice Hall, Englewood Cliffs, N.J., 1963, pp. 231-234. 
  2. [Ba] A. BANYAGA, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique (Comm. Math. Helv., Vol. 53, 1978, pp. 174-227). Zbl0393.58007MR80c:58005
  3. [BP] C. BESSAGA and A. PELCZYNSKI, Selected Topics in Infinite Dimensional Topology, P.W.N., Warszawa, 1975. Zbl0304.57001MR57 #17657
  4. [B] M. BROWN, A Mapping Theorem for Untriangulated Manifolds, in Topology of 3-Manifolds and Related Topics, M. K. FORT, Ed., Prentice Hall, Englewood Cliffs, N.J., 1963, pp. 92-94. MR28 #1599
  5. [CV] C. CHRISTENSON and W. VOXMAN, Aspects of Topology, Marcel Dekker Inc., New York, 1977. Zbl0347.54001MR58 #7521
  6. [DGS] M. DENKER, C. GRILLENBERGER and K. SIGMUND, Ergodic Theory on Compact Spaces (Lecture Notes in Math., No. 527, 1976, Springer-Verlag, Heidelberg. Zbl0328.28008MR56 #15879
  7. [EK] R. D. EDWARDS and R. KIRBY, Deformations of Spaces Spaces of Imbeddings (Ann. of Math., Vol. 93, 1971, pp. 63-88). Zbl0214.50303MR44 #1032
  8. [EW] S. EILENBERG and R. L. WILDER, Uniform Local Connectedness and Contractibility (Amer. J. Math., Vol. 64, 1942, pp. 613-622). Zbl0061.41103MR4,87e
  9. [Ep] D. EPSTEIN, Diff (M) is Simple ? in Symposium on Differential Equations and Dynamical Systems, Warwick, 1968-1969 (Lecture Notes in Math., No. 206, 1971, pp. 52-54, Springer-Verlag, New York). 
  10. [F] A. FATHI, Le groupe des transformations de [0, 1] qui préservent la mesure de Lebesgue est un groupe simple (Israël J. Math., Vol. 29, 1978, pp. 302-308). Zbl0375.28008MR58 #6156
  11. [FV] A. FATHI and Y. M. VISETTI, Structure du groupe des homéomorphismes préservant une mesure sur une variété compacte (C. R. Acad. Sc., T. 278, série A, 1977, pp. 849-852). Zbl0343.57019MR55 #6453
  12. [Fi] G. M. FISHER, On the Group of all Homeomorphisms of a Manifold (Trans. Amer. Math. Soc., Vol. 97, 1960, pp. 193-212). Zbl0144.22902MR22 #8487
  13. [He1] M. R. HERMAN, Sur le groupe des difféomorphismes du tore (Ann. Inst. Fourier, Vol. 23, 1973, pp. 75-86). Zbl0269.58004MR52 #11988
  14. [He2] M. R. HERMAN, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations (Publications mathématiques I.H.E.S., Vol. 49, 1979, pp. 1-233). Zbl0448.58019MR81h:58039
  15. [Hi] G. HIGMAN, On Infinite Simple Permutation Groups (Publications Math. Debrecen, Vol. 3, 1953, pp. 221-226). Zbl0057.25801MR17,234d
  16. [Hr] M. W. HIRSCH, Differential Topology, Graduate Texts in Math., Springer-Verlag, New York, Vol. 33, 1976. Zbl0356.57001MR56 #6669
  17. [Hu] J. F. P. HUDSON, Piecewise Linear Topology, W. A. Benjamin Inc., New York, 1969. Zbl0189.54507MR40 #2094
  18. [K] R. KIRBY, Stable Homeomorphisms and the Annulus Conjecture (Ann. Math., Vol. 89, 1969, pp. 575-582). Zbl0176.22004MR39 #3499
  19. [KS] R. KIRBY and L. C. SIEBENMANN, Foundational Essays on Topological Manifolds, Smoothings and Triangulations (Annals Math. Studies, Vol. 88, 1977, Princeton University Press, Princeton N.J.). Zbl0361.57004MR58 #31082
  20. [LM] R. LUKE and W. K. MASON, The Space of Homeomorphisms of a Compact Two-Manifold is an Absolute Neighborhood Retract (Trans. Amer. Math. Soc., 1972, pp. 275-285). Zbl0235.57002MR46 #849
  21. [LW] A. T. LUNDELL and S. WEINGRAM, The Topology of CW Complexes, Van Nostrand Reinhold, New York, 1969. Zbl0207.21704
  22. [Ma] J. MATHER, Commutators of Diffeomorphisms I and II (Comm. Math. Helv., Vol. 49, 1974, pp. 512-528 and Vol. 50, 1975, pp. 33-40). Zbl0299.58008
  23. [Mi] J. MILNOR, Morse Theory (Annals Math. Studies, Vol. 51, 1963, Princeton University Press, Princeton, N.J.). Zbl0108.10401MR29 #634
  24. [Mo] E. MOISE, Geometric Topology in Dimensions 2 and 3, Graduate Texts in Math., Springer-Verlag, New York, Vol. 47, 1977. Zbl0349.57001MR58 #7631
  25. [OU1] J. OXTOBY and S. ULAM, On the Equivalence of Any Set of First Category to a Set of Measure Zero (Fund. Math., Vol. 31, 1938, pp. 201-206). Zbl0019.29605JFM64.0185.02
  26. [OU2] J. OXTOBY and S. ULAM, Measure Preserving Homeomorphisms and Metrical Transitivity (Ann. Math., Vol. 42, 1941, pp. 874-920). Zbl0063.06074MR3,211b
  27. [Ru] T. RUSHING, Topological Embeddings, Academic Press, New York, 1973. Zbl0295.57003MR50 #1247
  28. [Sc] S. SCHWARTZMAN, Asymptotic Cycles (Ann. Math., Vol. 66, 1957, pp. 270-284). Zbl0207.22603MR19,568i
  29. [Sp] E. H. SPANIER, Algebraic Topology, McGraw-Hill, New York, 1966. Zbl0145.43303MR35 #1007
  30. [Th] W. THURSTON, On the Structure of the Group of Volume Preserving Diffeomorphisms (to appear). 
  31. [To] H. TORUNCZYK, Concerning Locally Homotopy Negligible Sets and Characterization of l²-Manifolds (Fund. Math., Vol. 101, 1978, pp. 93-110). Zbl0406.55003MR80g:57019

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.