×

On the group of all homeomorphisms of a manifold. (English) Zbl 0144.22902


Keywords:

topology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] J. M. Kister, Isotopies in 3-manifolds, Trans. Amer. Math. Soc. 97 (1960), 213 – 224. · Zbl 0096.37906
[2] Mary-Elizabeth Hamstrom and Eldon Dyer, Regular mappings and the space of homeomorphisms on a 2-manifold, Duke Math. J. 25 (1958), 521 – 531. · Zbl 0116.39903
[3] -, Regular mappings and the space of homeomorphisms on a 3-manifold, Amer. Math. Soc. Notices vol. 6 Part I (1959) Abstract 564-39, pp. 783-784.
[4] H. Tietze, Über stetige abbildungen einer quadrätflache auf sich selbst, Rend. Circ. Mat. Palermo vol. 38 (1914) pp. 247-304. · JFM 45.0729.01
[5] Hellmuth Kneser, Die Deformationssätze der einfach zusammenhängenden Flächen, Math. Z. 25 (1926), no. 1, 362 – 372 (German). · JFM 52.0573.01 · doi:10.1007/BF01283844
[6] R. Baer, Kurventypen auf Flächen, J. Reine Angew. Math. vol. 156 (1927) pp. 231-246. · JFM 53.0547.01
[7] -, Isotopie von Kurven auf orientbaren, geschlossenen Flächen und ihr Zusammenhang mit der topologischen Deformation der Flächen, J. Reine Angew. Math. vol. 159 (1928) pp. 101-116.
[8] J. Schreier and S. Ulam, Über topologischen Abbildungen der euklidischen Sphären, Fund. Math. vol. 23 (1934) pp. 102-118. · JFM 60.0529.02
[9] -, Eine Bemerkung über die Gruppe der topologischen Abbildungen der Kreislinie auf sich selbst, Studia Math. vol. 5 (1934) pp. 155-159. · Zbl 0013.05603
[10] Hellmuth Kneser, Reguläre Kurvenscharen auf den Ringflächen, Math. Ann. 91 (1924), no. 1-2, 135 – 154 (German). · JFM 50.0371.03 · doi:10.1007/BF01498385
[11] H. Poincaré, Mémoire sur les courbes définies par une équation differentielle, J. Math. Pures Appl. ser. 3 vol. 7 (1881) pp. 375-422; ser. 3 vol. 8 (1882) pp. 251-296; ser. 4 vol. 1 (1885) pp. 167-244. · JFM 13.0591.01
[12] S. Ulam and J. von Neumann, On the group of homeomorphisms of the surface of the sphere, Bull. Amer. Math. Soc. vol. 53 (1947) Abstract 283 p. 506.
[13] N. J. Fine and G. E. Schweigert, On the group of homeomorphisms of an arc, Ann. of Math. (2) 62 (1955), 237 – 253. · Zbl 0066.41305 · doi:10.2307/1969678
[14] R. D. Anderson, The algebraic simplicity of certain groups of homeomorphisms, Amer. J. Math. 80 (1958), 955 – 963. · Zbl 0090.38802 · doi:10.2307/2372842
[15] M. K. Fort Jr., A proof that the group of all homeomorphisms of the plane onto itself is locally arcwise connected, Proc. Amer. Math. Soc. 1 (1950), 59 – 62. · Zbl 0036.39003
[16] J. H. Roberts, Local arcwise connectivity in the space \( {H^n}\) of homeomorphisms of \( {S^n}\) onto itself, Summary of Lectures, Summer Institute on Set Theoretic Topology, Madison, Wisconsin, 1955, p. 100.
[17] A. Schoenflies, Beiträge zur Theorie der Punktmengen. III, Math. Ann. 62 (1906), no. 2, 286 – 328 (German). · JFM 37.0073.03 · doi:10.1007/BF01449982
[18] -, Die Entwickelung der Lehre von den Punktmannigfaltigkeiten, Leipzig, B. G. Teubner, 1908.
[19] B. v. Kerékjartó, Vorlesungen über Topologie, Berlin, Julius Springer, 1923.
[20] L. Antoine, Sur l’homeomorphie de deux figures et de leurs voisinages, Math. Pures Appl. ser. 8 vol. 4 (1921) pp. 221-325. · JFM 48.0650.01
[21] J. W. Alexander, An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. U.S.A. vol. 10 (1924) pp. 8-10.
[22] Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979 – 990. · Zbl 0033.13602 · doi:10.2307/1969408
[23] J. W. Alexander, On the subdivision of 3-space by a polyhedron, Proc. Nat. Acad. Sci. U.S.A. vol. 10 (1924) pp. 6-8. · JFM 50.0659.01
[24] Werner Graeub, Die semilinearen Abbildungen, Arch. Math. 2 (1950), 382 – 384 (German). · Zbl 0041.52303 · doi:10.1007/BF02036869
[25] Edwin E. Moise, Affine structures in 3-manifolds. II. Positional properties of 2-spheres, Ann. of Math. (2) 55 (1952), 172 – 176. · Zbl 0047.16802 · doi:10.2307/1969426
[26] R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145 – 158. · Zbl 0055.16802 · doi:10.2307/1969836
[27] R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465 – 483. · Zbl 0079.38805
[28] R. H. Bing, An alternative proof that 3-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37 – 65. · Zbl 0106.16604 · doi:10.2307/1970092
[29] Edwin E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96 – 114. · Zbl 0048.17102 · doi:10.2307/1969769
[30] O. Veblen, On the deformation of an n-cell, Proc. Nat. Acad. Sci. U.S.A. vol. 3 (1917) pp. 654-656. · JFM 46.0831.03
[31] J. W. Alexander, On the deformation of an n-cell, Proc. Nat. Acad. Sci. U.S.A. vol. 9 (1923) pp. 406-407.
[32] T. Radó, Über den Begriff der Riemannschen Flächen, Acta Szeged. vol. 2 (1925) pp. 101-121. · JFM 51.0273.01
[33] I. Gawehn, Über unberandete zweidimensionale Mannigfaltigkeiten, Math. Ann. vol. 98 (1927) pp. 321-354. · JFM 53.0556.04
[34] D. E. Sanderson, Isotopy in 3-manifolds. II. Fitting homeomorphisms by isotopy, Duke Math. J. 26 (1959), 387 – 396. · Zbl 0086.37704
[35] Edwin E. Moise, Affine structures in 3-manifolds. III. Tubular neighborhoods of linear graphs, Ann. of Math. (2) 55 (1952), 203 – 214. · Zbl 0047.16803 · doi:10.2307/1969774
[36] L. E. J. Brouwer, Über Abbildungen von Mannigfaltigkeiten, Math. Ann. vol. 71 (1912) pp. 97-115. · JFM 42.0417.01
[37] P. S. Alexandrov, Kombinatornaya Topologiya, vols. 1 and 2, 1947, trans. by H. Komm, Rochester, Graylock Press, 1956.
[38] Samuel Eilenberg and Norman Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey, 1952. · Zbl 0047.41402
[39] H. Seifert, Verschlingungsinvarianten, Sitzungsberichte Berlin Akad. (1933) pp. 811-828. · JFM 59.1238.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.