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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Constructing framed $ 4$-manifolds with given almost framed boundaries

Author: Steve J. Kaplan
Journal: Trans. Amer. Math. Soc. 254 (1979), 237-263
MSC: Primary 57N13; Secondary 57M25, 57N10
MathSciNet review: 539917
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Abstract: Two methods are presented for constructing framed 4-manifolds with given almost framed boundaries. The main tools are the ``moves'' of Kirby's calculus of framed links. A new description is given for the $ \mu $-in-variant of a knot and this description is used to study almost framed 3-manifolds.

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  • [1] M. Freedman and K. C. Kirby, A geometric proof of Rohlin's theorem, Proc. Sympos Pure Math., vol. 32, part 2, Amer. Math. Soc., Providence, R. I., 1976.
  • [2] C. McA. Gordon, Knots, homology spheres, and contractible 4-manifolds, Topology 14 (1975), 151-172. MR 0402762 (53:6576)
  • [3] J. Harer, A. Kas and R. Kirby, (to appear).
  • [4] N. Jacobson, Basic algebra. I, Freeman, San Francisco, Calif., 1974. MR 0356989 (50:9457)
  • [5] M. A. Kervaire and J. Milnor, On 2-spheres in 4-manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651-1657. MR 0133134 (24:A2968)
  • [6] R. C. Kirby, A calculus for framed links, Invent Math. 45 (1978), 35-55. MR 0467753 (57:7605)
  • [7] W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds, Ann. of Math. (2) 76 (1962), 531-540. MR 0151948 (27:1929)
  • [8] J. Milnor, Differentiable manifolds which are homotopy spheres, (mimeographed) Princeton, 1959.
  • [9] R. A. Robertello, An invariant of knot cobordism, Comm. Pure Appl. Math. 18 (1965), 543-555. MR 0182965 (32:447)
  • [10] D. Sullivan, On the intersection ring of compact 3-manifolds, Topology 14 (1975), 275-278. MR 0383415 (52:4296)

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Keywords: Framed 4-manifold, calculus of framed links, knots
Article copyright: © Copyright 1979 American Mathematical Society

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