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Proceedings of the American Mathematical Society

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

 
 

 

Ribbon concordance does not imply a degree one map


Author: Katura Miyazaki
Journal: Proc. Amer. Math. Soc. 108 (1990), 1055-1058
MSC: Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-1990-0994781-X
MathSciNet review: 994781
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Abstract: We give an example of classical knots $ {K_0},{K_1}$ sucn that (1) $ {K_1}$ is ribbon concordant to $ {K_0}$, (2) there are no degree one maps from the exterior of $ {K_1}$ in $ {S^3}$ to that of $ {K_0}$.


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

  • [1] P. Gilmer, Ribbon concordance and a partial order on $ S$-equivalence classes, Topology Appl. 18 (1984), 121-144. MR 769297 (86c:57006)
  • [2] C. Gordon, Ribbon concordance of knots in the $ 3$-sphere, Math. Ann. 257 (1981), 157-170. MR 634459 (83a:57007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0994781-X
Keywords: Ribbon concordance, degree one map, the ring of integers, Dedekind domain
Article copyright: © Copyright 1990 American Mathematical Society

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