Heegaard splittings of homology $3$-spheres
HTML articles powered by AMS MathViewer
- by Dean A. Neumann PDF
- Trans. Amer. Math. Soc. 180 (1973), 485-495 Request permission
Abstract:We investigate properties of Heegaard splittings of closed $3$-manifolds which are known for simply-connected manifolds and which might provide the basis for a general test for simple-connectivity. Our results are negative: each property considered is shown to hold in a wider class of manifolds.
- R. H. Bing and J. M. Martin, Cubes with knotted holes, Trans. Amer. Math. Soc. 155 (1971), 217–231. MR 278287, DOI 10.1090/S0002-9947-1971-0278287-4
- Wolfgang Haken, Various aspects of the three-dimensional Poincaré problem, Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969) Markham, Chicago, Ill., 1970, pp. 140–152. MR 0273624
- John Hempel, Construction of orientable $3$-manifolds, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 207–212. MR 0140115
- W. B. R. Lickorish, A representation of orientable combinatorial $3$-manifolds, Ann. of Math. (2) 76 (1962), 531–540. MR 151948, DOI 10.2307/1970373 J. M. Martin, (to appear).
- 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
- C. D. Papakyriakopoulos, A reduction of the Poincaré conjecture to group theoretic conjectures, Ann. of Math. (2) 77 (1963), 250–305. MR 145496, DOI 10.2307/1970216 H. Seifert and W. Threlfall, Lehrbuch der Topologie, Akad. Verlagsgesellschaft, Teubner, Leipzig, 1934. E. C. Zeeman, Seminar on combinatorial topology, Inst. Hautes Études Sci. Publ. Math., Paris, 1963.
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 180 (1973), 485-495
- MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0339185-2
- MathSciNet review: 0339185