A generalization of the Levine-Tristram link invariant
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- by Lawrence Smolinsky
- Trans. Amer. Math. Soc. 315 (1989), 205-217
- DOI: https://doi.org/10.1090/S0002-9947-1989-0931532-5
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Abstract:
Invariants to $m$-component links are defined and are shown to be link cobordism invariants under certain conditions. Examples are given.References
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. (2) 87 (1968), 546–604. MR 236952, DOI 10.2307/1970717
- Sylvain E. Cappell and Julius L. Shaneson, Link cobordism, Comment. Math. Helv. 55 (1980), no. 1, 20–49. MR 569244, DOI 10.1007/BF02566673
- D. Cooper, The universal abelian cover of a link, Low-dimensional topology (Bangor, 1979) London Math. Soc. Lecture Note Ser., vol. 48, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 51–66. MR 662427
- Patrick M. Gilmer, Configurations of surfaces in $4$-manifolds, Trans. Amer. Math. Soc. 264 (1981), no. 2, 353–380. MR 603768, DOI 10.1090/S0002-9947-1981-0603768-7
- Ki Hyoung Ko, Seifert matrices and boundary link cobordisms, Trans. Amer. Math. Soc. 299 (1987), no. 2, 657–681. MR 869227, DOI 10.1090/S0002-9947-1987-0869227-7
- J. Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969), 229–244. MR 246314, DOI 10.1007/BF02564525
- J. Levine, Invariants of knot cobordism, Invent. Math. 8 (1969), 98–110; addendum, ibid. 8 (1969), 355. MR 253348, DOI 10.1007/BF01404613
- John W. Milnor, Infinite cyclic coverings, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp. 115–133. MR 0242163
- L. Smolinsky, Doubly sliced knots which are not the double of a disk, Trans. Amer. Math. Soc. 298 (1986), no. 2, 723–732. MR 860389, DOI 10.1090/S0002-9947-1986-0860389-3 —, Casson-Gordon invariants of some $3$-fold branched covers of knots, Topology Appl. (to appear).
- A. G. Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969), 251–264. MR 248854, DOI 10.1017/s0305004100044947 O. J. Viro, Branched coverings of manifolds with boundary and link invariants. I, Math. USSR Izv. 7 (1973), 1239-1256.
- George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 315 (1989), 205-217
- MSC: Primary 57Q45; Secondary 57M25
- DOI: https://doi.org/10.1090/S0002-9947-1989-0931532-5
- MathSciNet review: 931532