Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Band-sums are ribbon concordant
to the connected sum

Author: Katura Miyazaki
Journal: Proc. Amer. Math. Soc. 126 (1998), 3401-3406
MSC (1991): Primary 57M25; Secondary 57Q60
MathSciNet review: 1451821
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that an arbitrary band-connected sum of two or more knots are ribbon concordant to the connected sum of these knots. As an application we consider which knot can be a nontrivial band-connected sum.

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

  • 1. M. Eudave-Muñoz; Prime knots obtained by band sums, Pac. J. Math. 139(1988), 53-57. MR 90i:57001
  • 2. D. Gabai; Genus is superadditive under band connected sum, Topology 26(1987), 209-210. MR 88h:57005
  • 3. C. McA. Gordon; Ribbon concordance of knots in the $3$-sphere, Math. Ann. 257(1981), 157-170. MR 83a:57007
  • 4. J. Hillman; On $L^2$-homology and asphericity, Israel J. Math. 99(1997), 271-283. CMP 98:01
  • 5. J. Howie and H. Short; The band-sum problem, J. London Math. Soc. 31(1985), 571-576. MR 87c:57004
  • 6. T. Kobayashi; Fibered links which are band connected sum of two links, In: Knots 90, (ed. A. Kawauchi), 1992, Walter de Gruyter, 9-23. MR 93m:57008
  • 7. T. Kobayashi; Knots which are prime on band connected sum, In: Proceedings of applied mathematics workshop vol. 4, (ed. K. H. Ko and G. T. Jin), 1994, KAIST, Korea, 79-89.
  • 8. Y. Marumoto; Some higher dimensional knots, Osaka J. Math. 24(1987), 759-783. MR 89e:57020
  • 9. K. Miyazaki; Non-simple, ribbon fibered knots, Thesis, University of Texas at Austin, 1990.
  • 10. E. S. Rapaport; Knot-like groups, Ann. of Math. Studies 84, 1975, Princeton Univ. Press, 119-133.
  • 11. M. Scharlemann; Smooth spheres in $R^4$ with four critical points are standard, Invent. Math. 79(1985), 125-141. MR 86e:57010
  • 12. M. Scharlemann; Sutured manifolds and generalized Thurston norms, J. Diff. Geom. 29(1987), 557-614. MR 90e:57021
  • 13. D. Silver; Growth rates of $n$-knots, Topology Appl. 42(1991), 217-230. MR 93a:57014
  • 14. D. Silver; On knot-like groups and ribbon concordance, J. Pure Appl. Algebra 82(1992), 99-105. MR 94a:57021
  • 15. A. Thompson; Property P for the band-connect sum of two knots, Topology 26(1987), 205-207. MR 88i:57004

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M25, 57Q60

Retrieve articles in all journals with MSC (1991): 57M25, 57Q60

Additional Information

Katura Miyazaki
Affiliation: Faculty of Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Tokyo 101, Japan

Keywords: Band-connected sum, concordance, ribbon concordance, fibered knot
Received by editor(s): November 12, 1996
Received by editor(s) in revised form: February 12, 1997
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society