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)

 
 

 

Unknotting links in $ S\sp{3}$ by maps


Author: Howard Lambert
Journal: Proc. Amer. Math. Soc. 60 (1976), 327-330
MSC: Primary 57A10; Secondary 57C45
DOI: https://doi.org/10.1090/S0002-9939-1976-0420624-1
MathSciNet review: 0420624
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: There exists a link $ {L_0} = {L_{01}} \cup {L_{02}}$ such that for no strongly 1-1 map f on $ {L_0}$ is it true that $ f({L_{01}}),f({L_{02}})$ are unknotted.


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

  • [1] R. H. Crowell, The derived module of a homomorphism, Advances in Math. 6 (1971), 210-238. MR 43 #2055. MR 0276308 (43:2055)
  • [2] Wolfgang Haken, Some results on surfaces in 3-manifolds, Studies in Modern Topology, Math. Assoc. Amer.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1968, pp. 39-98. MR 36 #7118. MR 0224071 (36:7118)
  • [3] J. Hempel, A surface in $ {S^3}$ is tame if it can be deformed into each complementary domain, Trans. Amer. Math. Soc. 111 (1964), 273-287. MR 28 #3409. MR 0160195 (28:3409)
  • [4] William Jaco and D. R. McMillan, Jr., Retracting three-manifolds onto finite graphs, Illinois J. Math. 14 (1970), 150-158. MR 41 #1026. MR 0256370 (41:1026)
  • [5] H. W. Lambert, Mapping cubes with holes onto cubes with handles, Illinois J. Math. 13 (1969), 606-615. MR 40 #2037. MR 0248787 (40:2037)
  • [6] C. D. Papakyriakopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1-26. MR 19, 761. MR 0090053 (19:761a)
  • [7] -, On solid tori, Proc. London Math. Soc. (3) 7 (1957), 281-299. MR 19, 441. MR 0087944 (19:441d)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57A10, 57C45

Retrieve articles in all journals with MSC: 57A10, 57C45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0420624-1
Keywords: Links, strongly 1-1 maps on links
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society