Structure of the group of homeomorphisms preserving a good measure on a compact manifold
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 13 (1980) no. 1, p. 45-93
@article{ASENS_1980_4_13_1_45_0,
     author = {Fathi, Albert},
     title = {Structure of the group of homeomorphisms preserving a good measure on a compact manifold},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 13},
     number = {1},
     year = {1980},
     pages = {45-93},
     doi = {10.24033/asens.1377},
     zbl = {0443.58011},
     mrnumber = {81k:58042},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1980_4_13_1_45_0}
}
Fathi, A. Structure of the group of homeomorphisms preserving a good measure on a compact manifold. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 13 (1980) no. 1, pp. 45-93. doi : 10.24033/asens.1377. http://www.numdam.org/item/ASENS_1980_4_13_1_45_0/

[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.

[Ba] A. Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique (Comm. Math. Helv., Vol. 53, 1978, pp. 174-227). | MR 80c:58005 | Zbl 0393.58007

[BP] C. Bessaga and A. Pelczynski, Selected Topics in Infinite Dimensional Topology, P.W.N., Warszawa, 1975. | MR 57 #17657 | Zbl 0304.57001

[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. | MR 28 #1599

[CV] C. Christenson and W. Voxman, Aspects of Topology, Marcel Dekker Inc., New York, 1977. | MR 58 #7521 | Zbl 0347.54001

[DGS] M. Denker, C. Grillenberger and K. Sigmund, Ergodic Theory on Compact Spaces (Lecture Notes in Math., No. 527, 1976, Springer-Verlag, Heidelberg. | MR 56 #15879 | Zbl 0328.28008

[EK] R. D. Edwards and R. Kirby, Deformations of Spaces Spaces of Imbeddings (Ann. of Math., Vol. 93, 1971, pp. 63-88). | MR 44 #1032 | Zbl 0214.50303

[EW] S. Eilenberg and R. L. Wilder, Uniform Local Connectedness and Contractibility (Amer. J. Math., Vol. 64, 1942, pp. 613-622). | MR 4,87e | Zbl 0061.41103

[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).

[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). | MR 58 #6156 | Zbl 0375.28008

[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). | MR 55 #6453 | Zbl 0343.57019

[Fi] G. M. Fisher, On the Group of all Homeomorphisms of a Manifold (Trans. Amer. Math. Soc., Vol. 97, 1960, pp. 193-212). | MR 22 #8487 | Zbl 0144.22902

[He1] M. R. Herman, Sur le groupe des difféomorphismes du tore (Ann. Inst. Fourier, Vol. 23, 1973, pp. 75-86). | Numdam | MR 52 #11988 | Zbl 0269.58004

[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). | Numdam | MR 81h:58039 | Zbl 0448.58019

[Hi] G. Higman, On Infinite Simple Permutation Groups (Publications Math. Debrecen, Vol. 3, 1953, pp. 221-226). | MR 17,234d | Zbl 0057.25801

[Hr] M. W. Hirsch, Differential Topology, Graduate Texts in Math., Springer-Verlag, New York, Vol. 33, 1976. | MR 56 #6669 | Zbl 0356.57001

[Hu] J. F. P. Hudson, Piecewise Linear Topology, W. A. Benjamin Inc., New York, 1969. | MR 40 #2094 | Zbl 0189.54507

[K] R. Kirby, Stable Homeomorphisms and the Annulus Conjecture (Ann. Math., Vol. 89, 1969, pp. 575-582). | MR 39 #3499 | Zbl 0176.22004

[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.). | MR 58 #31082 | Zbl 0361.57004

[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). | MR 46 #849 | Zbl 0235.57002

[LW] A. T. Lundell and S. Weingram, The Topology of CW Complexes, Van Nostrand Reinhold, New York, 1969. | Zbl 0207.21704

[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). | Zbl 0299.58008

[Mi] J. Milnor, Morse Theory (Annals Math. Studies, Vol. 51, 1963, Princeton University Press, Princeton, N.J.). | MR 29 #634 | Zbl 0108.10401

[Mo] E. Moise, Geometric Topology in Dimensions 2 and 3, Graduate Texts in Math., Springer-Verlag, New York, Vol. 47, 1977. | MR 58 #7631 | Zbl 0349.57001

[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). | JFM 64.0185.02 | Zbl 0019.29605

[OU2] J. Oxtoby and S. Ulam, Measure Preserving Homeomorphisms and Metrical Transitivity (Ann. Math., Vol. 42, 1941, pp. 874-920). | MR 3,211b | Zbl 0063.06074

[Ru] T. Rushing, Topological Embeddings, Academic Press, New York, 1973. | MR 50 #1247 | Zbl 0295.57003

[Sc] S. Schwartzman, Asymptotic Cycles (Ann. Math., Vol. 66, 1957, pp. 270-284). | MR 19,568i | Zbl 0207.22603

[Sp] E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. | MR 35 #1007 | Zbl 0145.43303

[Th] W. Thurston, On the Structure of the Group of Volume Preserving Diffeomorphisms (to appear).

[To] H. Torunczyk, Concerning Locally Homotopy Negligible Sets and Characterization of l²-Manifolds (Fund. Math., Vol. 101, 1978, pp. 93-110). | MR 80g:57019 | Zbl 0406.55003