Homotopy in homeomorphism spaces, $TOP$ and $PL$
HTML articles powered by AMS MathViewer
- by Mary-Elizabeth Hamstrom PDF
- Bull. Amer. Math. Soc. 80 (1974), 207-230
References
- Tadatoshi Akiba, On the homotopy type of $\textrm {PL}_{2}$, J. Fac. Sci. Univ. Tokyo Sect. I 14 (1967), 197–204. MR 226673
- Tadatoshi Akiba, Homotopy types of some $PL$ complexes, Bull. Amer. Math. Soc. 77 (1971), 1060–1062. MR 326747, DOI 10.1090/S0002-9904-1971-12865-3 3. J. W. Alexander, On the deformation of an n-cell, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 406-407.
- R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465–483. MR 87090
- R. H. Bing, An alternative proof that $3$-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37–65. MR 100841, DOI 10.2307/1970092
- William Browder, Open and closed disk bundles, Ann. of Math. (2) 83 (1966), 218–230. MR 189058, DOI 10.2307/1970428
- Marston Morse, A reduction of the Schoenflies extension problem, Bull. Amer. Math. Soc. 66 (1960), 113–115. MR 117694, DOI 10.1090/S0002-9904-1960-10420-X
- J. C. Cantrell and T. B. Rushing, On low-codimensional taming, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp. 353–357. MR 0273622
- A. V. Černavskiĭ, Local contractibility of the group of homeomorphisms of a manifold. , Mat. Sb. (N.S.) 79 (121) (1969), 307–356 (Russian). MR 0259925
- A. V. Černavskiĭ, Topological embeddings of manifolds, Dokl. Akad. Nauk SSSR 187 (1969), 1247–1250 (Russian). MR 0259918
- E. H. Connell, Approximating stable homeomorphisms by piecewise linear ones, Ann. of Math. (2) 78 (1963), 326–338. MR 154289, DOI 10.2307/1970346
- Robert Craggs, Building Cartesian products of surfaces with $[0,\,1]$, Trans. Amer. Math. Soc. 144 (1969), 391–425. MR 250314, DOI 10.1090/S0002-9947-1969-0250314-0
- Robert Craggs, Small ambient isotopies of a $3$-manifold which transform one embedding of a polyhedron into another, Fund. Math. 68 (1970), 225–256. MR 275440, DOI 10.4064/fm-68-3-225-256
- Robert D. Edwards and Robion C. Kirby, Deformations of spaces of imbeddings, Ann. of Math. (2) 93 (1971), 63–88. MR 283802, DOI 10.2307/1970753
- Robert D. Edwards, The equivalence of close piecewise linear embeddings, General Topology and Appl. 5 (1975), 147–180. MR 370603
- Bjorn Friberg, A topological proof of a theorem of Kneser, Proc. Amer. Math. Soc. 39 (1973), 421–426. MR 321124, DOI 10.1090/S0002-9939-1973-0321124-7
- David B. Gauld, The canonical Schoenflies theorem, Proc. Amer. Math. Soc. 27 (1971), 603–612. MR 279786, DOI 10.1090/S0002-9939-1971-0279786-7
- P. R. Hall, On the space of homeomorphisms of $E^{3}$, Bull. Amer. Math. Soc. 75 (1969), 788–789. MR 244937, DOI 10.1090/S0002-9904-1969-12291-3 19. Eldon Dyer and Mary-Elizabeth Hamstrom, Completely regular mappings, Fund. Math. 45 (1957), 103-118. MR 19, 1187.
- Mary-Elizabeth Hamstrom and Eldon Dyer, Regular mappings and the space of homeomorphisms on a 2-manifold, Duke Math. J. 25 (1958), 521–531. MR 96202
- Mary-Elizabeth Hamstrom, Regular mappings whose inverses are $3$-cells, Amer. J. Math. 82 (1960), 393–429. MR 117700, DOI 10.2307/2372966
- Mary-Elizabeth Hamstrom, Regular mappings and the space of homeomorphisms on a $3$-manifold, Mem. Amer. Math. Soc. 40 (1961), 42. MR 152999
- Mary-Elizabeth Hamstrom, Some global properties of the space of homeomorphisms on a disc with holes, Duke Math. J. 29 (1962), 657–662. MR 143185
- Mary-Elizabeth Hamstrom, The space of homeomorphisms on a torus, Illinois J. Math. 9 (1965), 59–65. MR 170334
- Mary-Elizabeth Hamstrom, Homotopy properties of the space of homeomorphisms on $P^{2}$ and the Klein bottle, Trans. Amer. Math. Soc. 120 (1965), 37–45. MR 184234, DOI 10.1090/S0002-9947-1965-0184234-3
- Mary-Elizabeth Hamstrom, Homotopy groups of the space of homeomorphisms on a $2$-manifold, Illinois J. Math. 10 (1966), 563–573. MR 202140
- Mary-Elizabeth Hamstrom, Regular mappings: A survey, Proc. First Conf. on Monotone Mappings and Open Mappings (SUNY at Binghamton, Binghamton, N.Y., 1970) State Univ. of New York at Binghamton, Binghamton, N.Y., 1971, pp. 238–254. MR 0275383
- Mary-Elizabeth Hamstrom, Completely regular mappings whose inverses have $\textrm {LC}^{0}$ homeomorphism group: A correction, Proc. First Conf. on Monotone Mappings and Open Mappings (SUNY at Binghamton, Binghamton, N.Y., 1970) State Univ. of New York at Binghamton, Binghamton, N.Y., 1971, pp. 255–260. MR 0278270 29. William E. Haver, Function spaces on manifolds, Notices Amer. Math. Soc. 19 (1972), A803. Abstract #699-G4.
- J. F. P. Hudson and E. C. Zeeman, On combinatorial isotopy, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 69–94. MR 163318
- John F. P. Hudson, Extending piecewise-linear isotopies, Proc. London Math. Soc. (3) 16 (1966), 651–668. MR 202147, DOI 10.1112/plms/s3-16.1.651
- J. F. P. Hudson, Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, 1969. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. MR 0248844
- William Huebsch and Marston Morse, The dependence of the Schoenflies extension on an accessory parameter (the topological case), Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1036–1037. MR 182957, DOI 10.1073/pnas.50.6.1036 34. Marvin Israel, Dissertation, University of Illinois at Urbana-Champaign (in preparation).
- Robion C. Kirby, Stable homeomorphisms and the annulus conjecture, Ann. of Math. (2) 89 (1969), 575–582. MR 242165, DOI 10.2307/1970652 36. Robion C. Kirby, Lectures on triangulations of manifolds, mimeographed notes, UCLA, 1969.
- J. M. Kister, Isotopies in $3$-manifolds, Trans. Amer. Math. Soc. 97 (1960), 213–224. MR 120628, DOI 10.1090/S0002-9947-1960-0120628-5
- J. M. Kister, Microbundles are fibre bundles, Ann. of Math. (2) 80 (1964), 190–199. MR 180986, DOI 10.2307/1970498
- Hellmuth Kneser, Die Deformationssätze der einfach zusammenhängenden Flächen, Math. Z. 25 (1926), no. 1, 362–372 (German). MR 1544816, DOI 10.1007/BF01283844
- N. H. Kuiper and R. K. Lashof, Microbundles and bundles. II. Semisimplical theory, Invent. Math. 1 (1966), 243–259. MR 216507, DOI 10.1007/BF01452244
- A. I. Markuševič, Teoriya analitičeskih funkciĭ, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1950 (Russian). MR 0036301
- J. Peter May, Simplicial objects in algebraic topology, Van Nostrand Mathematical Studies, No. 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0222892
- G. S. McCarty Jr., Homeotopy groups, Trans. Amer. Math. Soc. 106 (1963), 293–304. MR 145531, DOI 10.1090/S0002-9947-1963-0145531-9
- Ernest Michael, Continuous selections. III, Ann. of Math. (2) 65 (1957), 375–390. MR 83715, DOI 10.2307/1969969 45. E. E. Moise, Affine structures in 3-manifolds. IV, V. Piecewise linear approximations of homeomorphisms, The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 55 (1952), 215-222; ibid. 56 (1952), 96-114. MR 13, 765; 14, 72. 46. C. Morlet, Plongements et automorphismes des variétés, Mimeographed notes, Collège de France, 1969.
- H. R. Morton, The space of homeomorphisms of a disc with $n$ holes, Illinois J. Math. 11 (1967), 40–48. MR 205233
- Louis V. Quintas, The homotopy groups of the space of homeomorphisms of a multiply punctured surface, Illinois J. Math. 9 (1965), 721–725. MR 184207 49. Louis V. Quintas, Solved and unsolved problems in the computation of homeotopy groups of 2-manifolds, Trans. N.Y. Acad. Sci. Ser. II 30 (1968), 919-938. 50. J. H. Roberts, Local arcwise connectivity in the space H, Summary of lectures and seminars, Summer Institute on Set Theoretic Topology, Madison, Wisconsin, 1955, revised 1958, 110.
- C. P. Rourke and B. J. Sanderson, Block bundles. I, Ann. of Math. (2) 87 (1968), 1–28. MR 226645, DOI 10.2307/1970591
- T. Benny Rushing, Topological embeddings, Pure and Applied Mathematics, Vol. 52, Academic Press, New York-London, 1973. MR 0348752
- D. E. Sanderson, Isotopy in 3-manifolds. II. Fitting homeomorphisms by isotopy, Duke Math. J. 26 (1959), 387–396. MR 107231
- G. P. Scott, The space of homeomorphisms of a $2$-manifold, Topology 9 (1970), 97–109. MR 264676, DOI 10.1016/0040-9383(70)90053-4 55. G. P. Scott, On the homotopy type of PL3, mimeographed, University of Liverpool, 1970.
- C. L. Seebeck III, Collaring and $(n-1)$-manifold in an $n$-manifold, Trans. Amer. Math. Soc. 148 (1970), 63–68. MR 258045, DOI 10.1090/S0002-9947-1970-0258045-6
- Neal R. Wagner, The space of retractions of the $2$-sphere and the annulus, Trans. Amer. Math. Soc. 158 (1971), 319–329. MR 279763, DOI 10.1090/S0002-9947-1971-0279763-0
- Paul A. White, Regular convergence, Bull. Amer. Math. Soc. 60 (1954), 431–443. MR 66639, DOI 10.1090/S0002-9904-1954-09826-9
- Hassler Whitney, Regular families of curves, Ann. of Math. (2) 34 (1933), no. 2, 244–270. MR 1503106, DOI 10.2307/1968202 60. G. T. Whyburn, On sequences and limiting sets, Fund. Math. 25 (1935), 408-426.
- Perrin Wright, Covering isotopies of $M^{n-1}$ in $N^{n}$, Proc. Amer. Math. Soc. 29 (1971), 591–598. MR 281215, DOI 10.1090/S0002-9939-1971-0281215-4
Additional Information
- Journal: Bull. Amer. Math. Soc. 80 (1974), 207-230
- MSC (1970): Primary 58D10, 57A35, 57C35; Secondary 57C55, 57E05, 55E99
- DOI: https://doi.org/10.1090/S0002-9904-1974-13433-6
- MathSciNet review: 0334262