Bulletin of the American Mathematical Society

Acyclicity in three-manifolds

D. R. McMillan, Jr.

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 76, Number 5 (1970), 942-964.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183532191

Mathematical Reviews number (MathSciNet)
MR0270380

Zentralblatt MATH identifier
0198.56303

Subjects
Primary: 5705
Secondary: 5460 5478 6560 5568

Citation

McMillan, D. R. Acyclicity in three-manifolds. Bull. Amer. Math. Soc. 76 (1970), no. 5, 942--964. https://projecteuclid.org/euclid.bams/1183532191


Export citation

References

  • 1. S. Armentrout, Cellular decompositions of 3-manifolds that yield 3-manifolds, Bull. Amer. Math. Soc. 75 (1969), 453-456. MR 39 #935.
  • 2. S. Armentrout, UV properties of compact sets, Trans. Amer. Math. Soc. 143 (1969), 487-498.
  • 3. S. Armentrout, Homotopy properties of decomposition spaces, Trans. Amer. Math. Soc. 143 (1969), 499-507.
  • 4. S. Armentrout, Shrinkability of certain decompositions of E3 that yield E3, Illinois J. Math. 13 (1969), 700-706.
  • 5. S. Armentrout, L. L. Lininger and D. V. Meyer, Equivalent decomposition of R3, Pacific J. Math. 24 (1968), 205-227. MR 36#7117.
  • 6. S. Armentrout and T. M. Price, Decompositions into compact sets with UV properties, Trans. Amer. Math. Soc. 141 (1969), 433-442.
  • 7. R. H. Bing, Conditions under which monotone decompositions of E3 are simply connected, Bull. Amer. Math. Soc. 63 (1957), 143. Abstract #325.
  • 8. K. Borsuk, Theory of retracts, Monografie Mat., Tom. 44, PWN, Warsaw, 1967. MR 35 #7306.
  • 9. K. Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), 223-254. MR 37 #4811.
  • 10. J. H. Case and R. E. Chamberlin, Characterizations of tree-like continua, Pacific J. Math. 10 (1960), 73-84. MR 22 #1868.
  • 11. M. L. Curtis, Shrinking continua in 3-space, Proc. Cambridge Philos. Soc. 57 (1961), 432-433. MR 22 #11391.
  • 12. W. Haken, Some results on surfaces in 3-manifolds, Studies in Modern Topology, Math. Assoc. Amer, (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1968, pp. 39-98. MR 36 #7118.
  • 13. J. P. Hempel, A surface in S3 is tame if it can be deformed into each complementary domain, Trans. Amer. Math. Soc. 111 (1964), 273-287. MR 28 #3409.
  • 14. D. M. Hyman, ANR divisors and absolute neighborhood contractibility, Fund. Math. 62 (1968), 61-73. MR 37 #4771.
  • 15. V. P. Kompaniec and A. V. Černavskiĭ, Equivalence of two classes of sphere mappings, Dokl. Akad. Nauk SSSR 169 (1966), 1266-1268= Soviet Math. Dokl. 7 (1966), 1083-1085. MR 39 #2133.
  • 16. G. Kozlowski, Factorization of certain maps up to homotopy, Proc. Amer. Math. Soc. 21 (1969), 88-92. MR 38 #6588.
  • 17. K. W. Kwun and F. Raymond, Almost acyclic maps of manifolds, Amer. J. Math. 86 (1964), 638-650. MR 32 #1712.
  • 18. R. C. Lacher, Cell-like mappings. I, Pacific J. Math. 30 (1969), 717-731.
  • 19. R. C. Lacher, Cellularity criteria for maps, Michigan Math. J (to appear).
  • 20. H. W. Lambert, Replacing certain maps of 3-manifolds by homeomorphisms, Proc. Amer. Math. Soc. 23 (1969), 676-678.
  • 21. W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol, XIII, Interscience, New York, 1966. MR 34 #7617.
  • 22. J. Martin, The sum of two crumpled cubes, Michigan Math J. 13 (1966), 147-151. MR 32 #8324.
  • 23. B. Mazur, A note on some contractible 4-manifolds, Ann. of Math. (2) 73 (1961), 221-228. MR 23 #A2873.
  • 24. D. R. McMillan, Jr., A criterion for cellularity in a manifold, Ann. of Math. (2) 79 (1964), 327-337. MR 28 #4528.
  • 25. D. R. McMillan, Jr., Strong homotopy equivalence of 3-manifolds, Bull. Amer. Math. Soc. 73 (1967), 718-722. MR 37 #4817.
  • 26. D. R. McMillan, Jr., Compact, acyclic subsets of three-manifolds, Michigan Math. J. 16 (1969), 129-136. MR 39 #4822.
  • 27. T. M. Price, A necessary condition that a cellular upper semicontinuous decomposition of En yield En, Trans, Amer. Math. Soc. 122 (1966), 427-435. MR 33 #1843.
  • 28. L. C. Siebenmann, On detecting Euclidean space homotopically among topological manifolds, Invent. Math. 6 (1968), 245-261. MR 38 #6601.
  • 29. E. G. Skljarenko, Almost acyclic mappings, Mat. Sb. 75 (117) (1968), 296-302 = Math. USSR Sb. 4 (1968), 267-272. MR 37 #4806.
  • 30. S. Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957), 604-610. MR 19, 302.
  • 31. E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 35 #1007.
  • 32. J. Stallings, Homology and central series of groups, J. Algebra 2 (1965), 170-181. MR 31 #232.
  • 33. M. A. Štan'ko, Imbedding of tree-like compacta in E3, Mat. Sb. 75 (117) (1968), 211-224 = Math. USSR Sb. 4 (1968), 191-202. MR 36 #5918.
  • 34. G. T. Whyburn, Compactness of certain mappings, Amer. J. Math. 81 (1959), 306-314. MR 22 #1881.
  • 35. A. Wright, Monotone mappings of compact 3-manifolds, Ph.D. Thesis, University of Wisconsin, Madison, 1969.