Doubly sliced knots which are not the double of a disk
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- by L. Smolinsky PDF
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Abstract:
In this paper we show that double disk knots can be distinguished from general doubly sliced knots in dimensions $4n + 1$.References
- Selman Akbulut and Robion Kirby, Branched covers of surfaces in $4$-manifolds, Math. Ann. 252 (1979/80), no. 2, 111–131. MR 593626, DOI 10.1007/BF01420118
- Kouhei Asano, Yoshihiko Marumoto, and Takaaki Yanagawa, Ribbon knots and ribbon disks, Osaka Math. J. 18 (1981), no. 1, 161–174. MR 609984
- 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
- A. J. Casson and C. McA. Gordon, On slice knots in dimension three, Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976) Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, R.I., 1978, pp. 39–53. MR 520521
- 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
- Patrick M. Gilmer and Charles Livingston, On embedding $3$-manifolds in $4$-space, Topology 22 (1983), no. 3, 241–252. MR 710099, DOI 10.1016/0040-9383(83)90011-3
- 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, Invariants of knot cobordism, Invent. Math. 8 (1969), 98–110; addendum, ibid. 8 (1969), 355. MR 253348, DOI 10.1007/BF01404613
- J. Levine, Doubly sliced knots and doubled disk knots, Michigan Math. J. 30 (1983), no. 2, 249–256. MR 718271, DOI 10.1307/mmj/1029002856
- Daniel Ruberman, Doubly slice knots and the Casson-Gordon invariants, Trans. Amer. Math. Soc. 279 (1983), no. 2, 569–588. MR 709569, DOI 10.1090/S0002-9947-1983-0709569-5 L. Smolinsky, Double disk knots and a link invariant, Ph.D. Thesis, Brandeis University, 1985. —, A generalization of the Levine-Tristram link invariant, in preparation.
- D. W. Sumners, Invertible knot cobordisms, Comment. Math. Helv. 46 (1971), 240–256. MR 290351, DOI 10.1007/BF02566842
- A. G. Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969), 251–264. MR 248854, DOI 10.1017/s0305004100044947 O. Ja. Viro, Branched coverings of manifolds with boundary and link invariants. I, Math. USSR Izv. 7 (1973), 1239-1256.
- Don Bernard Zagier, Equivariant Pontrjagin classes and applications to orbit spaces. Applications of the $G$-signature theorem to transformation groups, symmetric products and number theory, Lecture Notes in Mathematics, Vol. 290, Springer-Verlag, Berlin-New York, 1972. MR 0339202
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 298 (1986), 723-732
- MSC: Primary 57Q45; Secondary 57Q60
- DOI: https://doi.org/10.1090/S0002-9947-1986-0860389-3
- MathSciNet review: 860389