Band-sums are ribbon concordant to the connected sum
HTML articles powered by AMS MathViewer
- by Katura Miyazaki PDF
- Proc. Amer. Math. Soc. 126 (1998), 3401-3406 Request permission
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
- Mario Eudave Muñoz, Prime knots obtained by band sums, Pacific J. Math. 139 (1989), no. 1, 53–57. MR 1010784, DOI 10.2140/pjm.1989.139.53
- David Gabai, Genus is superadditive under band connected sum, Topology 26 (1987), no. 2, 209–210. MR 895573, DOI 10.1016/0040-9383(87)90061-9
- C. McA. Gordon, Ribbon concordance of knots in the $3$-sphere, Math. Ann. 257 (1981), no. 2, 157–170. MR 634459, DOI 10.1007/BF01458281
- J. Hillman; On $L^2$-homology and asphericity, Israel J. Math. 99(1997), 271–283.
- James Howie and Hamish Short, The band-sum problem, J. London Math. Soc. (2) 31 (1985), no. 3, 571–576. MR 812788, DOI 10.1112/jlms/s2-31.3.571
- Tsuyoshi Kobayashi, Fibered links which are band connected sum of two links, Knots 90 (Osaka, 1990) de Gruyter, Berlin, 1992, pp. 9–23. MR 1177410
- 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.
- Yoshihiko Marumoto, Some higher-dimensional knots, Osaka J. Math. 24 (1987), no. 4, 759–783. MR 927060
- K. Miyazaki; Non-simple, ribbon fibered knots, Thesis, University of Texas at Austin, 1990.
- E. S. Rapaport; Knot-like groups, Ann. of Math. Studies 84, 1975, Princeton Univ. Press, 119-133.
- Martin Scharlemann, Smooth spheres in $\textbf {R}^4$ with four critical points are standard, Invent. Math. 79 (1985), no. 1, 125–141. MR 774532, DOI 10.1007/BF01388659
- Martin Scharlemann, Sutured manifolds and generalized Thurston norms, J. Differential Geom. 29 (1989), no. 3, 557–614. MR 992331
- Daniel S. Silver, Growth rates of $n$-knots, Topology Appl. 42 (1991), no. 3, 217–230. MR 1137948, DOI 10.1016/0166-8641(91)90123-4
- D. S. Silver, On knot-like groups and ribbon concordance, J. Pure Appl. Algebra 82 (1992), no. 1, 99–105. MR 1181096, DOI 10.1016/0022-4049(92)90013-6
- Abigail Thompson, Property $\textrm {P}$ for the band-connect sum of two knots, Topology 26 (1987), no. 2, 205–207. MR 895572, DOI 10.1016/0040-9383(87)90060-7
Additional Information
- Katura Miyazaki
- Affiliation: Faculty of Engineering, Tokyo Denki University, 2-2 Kanda-Nishikicho, Tokyo 101, Japan
- Email: miyazaki@cck.dendai.ac.jp
- Received by editor(s): November 12, 1996
- Received by editor(s) in revised form: February 12, 1997
- Communicated by: Ronald A. Fintushel
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3401-3406
- MSC (1991): Primary 57M25; Secondary 57Q60
- DOI: https://doi.org/10.1090/S0002-9939-98-04352-4
- MathSciNet review: 1451821