Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 
 

 

Doubly sliced knots which are not the double of a disk


Author: L. Smolinsky
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that double disk knots can be distinguished from general doubly sliced knots in dimensions $ 4n + 1$.


References [Enhancements On Off] (What's this?)

  • [1] S. Akbulut and R. Kirby, Branched covers of surfaces in $ 4$-manifolds, Math. Ann. 252 (1980), 111-132. MR 593626 (82j:57001)
  • [2] K. Asano, Y. Marumoto and T. Yanagawa, Ribbon knots and ribbon disks, Osaka J. Math. 18 (1981), 161-174. MR 609984 (82d:57010)
  • [3] M. F. Atiyah and I. M. Singer, The index of elliptic operators: III, Ann. of Math. 87 (1968), 546-604. MR 0236952 (38:5245)
  • [4] A. Casson and C. Gordon, On slice knots in dimension three, Proc. Sympos. Pure Math. vol. 32, Amer. Math. Soc., Providence, R.I., 1978. MR 520521 (81g:57003)
  • [5] P. Gilmer, Configurations of surfaces in $ 4$-manifolds, Trans. Amer. Math. Soc. 264 (1981), 353-380. MR 603768 (83h:57027)
  • [6] P. Gilmer and C. Livingston, On embedding $ 3$-manifolds in $ 4$-space, Topology 22 (1983), 241-252. MR 710099 (85b:57035)
  • [7] Ki Hyoung Ko, Seifert matrices and boundary link cobordisms, preprint. MR 869227 (88h:57018)
  • [8] J. Levine, Invariants of knot cobordism, Invent. Math. 8 (1969), 98-110. MR 0253348 (40:6563)
  • [9] -, Doubly sliced knots and doubled disk knots, Michigan Math. J. 30 (1983), 249-256. MR 718271 (85h:57024)
  • [10] D. Ruberman, Doubly sliced knots and the Casson-Gordon invariants, Trans. Amer. Math. Soc. 279 (1983), 569-588. MR 709569 (85e:57025)
  • [11] L. Smolinsky, Double disk knots and a link invariant, Ph.D. Thesis, Brandeis University, 1985.
  • [12] -, A generalization of the Levine-Tristram link invariant, in preparation.
  • [13] D. W. Sumners, Invertible knot cobordisms, Comment. Math. Helv. 46 (1971), 240-256. MR 0290351 (44:7535)
  • [14] A. G. Tristram, Some cobordism invariants for links, Proc. Cambridge Philos. Soc. 66 (1969), 251-264. MR 0248854 (40:2104)
  • [15] O. Ja. Viro, Branched coverings of manifolds with boundary and link invariants. I, Math. USSR Izv. 7 (1973), 1239-1256.
  • [16] D. Zagier, Equivariant Pontrjagin classes and applications to orbit spaces, Lecture Notes in Math., vol. 290, Springer-Verlag, New York, 1972. MR 0339202 (49:3965)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57Q45, 57Q60

Retrieve articles in all journals with MSC: 57Q45, 57Q60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0860389-3
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society