Acyclicity in three-manifolds
HTML articles powered by AMS MathViewer
- by D. R. McMillan Jr. PDF
- Bull. Amer. Math. Soc. 76 (1970), 942-964
References
- Steve Armentrout, Cellular decompositions of $3$-manifolds that yield $3$-manifolds, Bull. Amer. Math. Soc. 75 (1969), 453–456. MR 239578, DOI 10.1090/S0002-9904-1969-12218-4
- Steve Armentrout, $\textrm {UV}$ properties of compact sets, Trans. Amer. Math. Soc. 143 (1969), 487–498. MR 273573, DOI 10.1090/S0002-9947-1969-0273573-7
- Steve Armentrout, Homotopy properties of decomposition spaces, Trans. Amer. Math. Soc. 143 (1969), 499–507. MR 273574, DOI 10.1090/S0002-9947-1969-0273574-9
- Steve Armentrout, Shrinkability of certain decompositions of $E^{3}$ that yield $E^{3}$, Illinois J. Math. 13 (1969), 700–706. MR 246273
- Steve Armentrout, Lloyd L. Lininger, and Donald V. Meyer, Equivalent decomposition of $R^{3}$, Pacific J. Math. 24 (1968), 205–227. MR 224070
- Steve Armentrout and Thomas M. Price, Decompositions into compact sets with $UV$ properties, Trans. Amer. Math. Soc. 141 (1969), 433–442. MR 244994, DOI 10.1090/S0002-9947-1969-0244994-3 7. R. H. Bing, Conditions under which monotone decompositions of E3 are simply connected, Bull. Amer. Math. Soc. 63 (1957), 143. Abstract #325.
- Karol Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
- Karol Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223–254. MR 229237, DOI 10.4064/fm-62-3-223-254
- J. H. Case and R. E. Chamberlin, Characterizations of tree-like continua, Pacific J. Math. 10 (1960), 73–84. MR 111000
- M. L. Curtis, Shrinking continua in $3$-space, Proc. Cambridge Philos. Soc. 57 (1961), 432–433. MR 120641
- Wolfgang Haken, Some results on surfaces in $3$-manifolds, Studies in Modern Topology, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1968, pp. 39–98. MR 0224071
- John Hempel, A surface in $S^{3}$ is tame if it can be deformed into each complementary domain, Trans. Amer. Math. Soc. 111 (1964), 273–287. MR 160195, DOI 10.1090/S0002-9947-1964-0160195-7
- D. M. Hyman, $\textrm {ANR}$ divisors and absolute neighborhood contractability, Fund. Math. 62 (1968), 61–73. MR 229197, DOI 10.4064/fm-62-1-61-73
- V. P. Kompaniec and A. V. Černavskiĭ, Equivalence of two classes of sphere mappings, Soviet Math. Dokl. 7 (1966), 1083–1085. MR 0240788
- George Kozlowski, Factorization of certain maps up to homotopy, Proc. Amer. Math. Soc. 21 (1969), 88–92. MR 238312, DOI 10.1090/S0002-9939-1969-0238312-X
- Kyung Whan Kwun and Frank Raymond, Almost acyclic maps on manifolds, Amer. J. Math. 86 (1964), 638–650. MR 184239, DOI 10.2307/2373028
- R. C. Lacher, Cell-like mappings. I, Pacific J. Math. 30 (1969), 717–731. MR 251714
- R. C. Lacher, Cellularity criteria for maps, Michigan Math. J. 17 (1970), 385–396. MR 279818
- H. W. Lambert, Replacing certain maps of $3$-manifolds by homeomorphisms, Proc. Amer. Math. Soc. 23 (1969), 676–678. MR 256402, DOI 10.1090/S0002-9939-1969-0256402-2
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
- Joseph Martin, The sum of two crumpled cubes, Michigan Math. J. 13 (1966), 147–151. MR 190914
- Barry Mazur, A note on some contractible $4$-manifolds, Ann. of Math. (2) 73 (1961), 221–228. MR 125574, DOI 10.2307/1970288
- D. R. McMillan Jr., A criterion for cellularity in a manifold, Ann. of Math. (2) 79 (1964), 327–337. MR 161320, DOI 10.2307/1970548
- D. R. McMillan Jr., Strong homotopy equivalence of $3$-manifolds, Bull. Amer. Math. Soc. 73 (1967), 718–722. MR 229243, DOI 10.1090/S0002-9904-1967-11843-3
- D. R. McMillan Jr., Compact, acyclic subsets of three-manifolds, Michigan Math. J. 16 (1969), 129–136. MR 243501
- T. M. Price, A necessary condition that a cellular upper semi-continuous decomposition of $E^{n}$ yield $E^{n}$, Trans. Amer. Math. Soc. 122 (1966), 427–435. MR 193627, DOI 10.1090/S0002-9947-1966-0193627-0
- L. C. Siebenmann, On detecting Euclidean space homotopically among topological manifolds, Invent. Math. 6 (1968), 245–261. MR 238325, DOI 10.1007/BF01404826
- E. G. Skljarenko, Almost acyclic mappings, Mat. Sb. (N.S.) 75 (117) (1968), 296–302 (Russian). MR 0229232
- Stephen Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957), 604–610. MR 87106, DOI 10.1090/S0002-9939-1957-0087106-9
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- John Stallings, Homology and central series of groups, J. Algebra 2 (1965), 170–181. MR 175956, DOI 10.1016/0021-8693(65)90017-7
- M. A. Štan′ko, The imbedding of tree-like compacta in $E^{3}$, Mat. Sb. (N.S.) 75 (117) (1968), 211–224 (Russian). MR 0222868
- G. T. Whyburn, Compactness of cetain mappings, Amer. J. Math. 81 (1959), 306–314. MR 111014, DOI 10.2307/2372746 35. A. Wright, Monotone mappings of compact 3-manifolds, Ph.D. Thesis, University of Wisconsin, Madison, 1969.
Additional Information
- Journal: Bull. Amer. Math. Soc. 76 (1970), 942-964
- MSC (1970): Primary 5705; Secondary 5460, 5478, 6560, 5568
- DOI: https://doi.org/10.1090/S0002-9904-1970-12510-1
- MathSciNet review: 0270380