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Essential maps and embeddings of annuli in nonorientable $ M\sp{3}$


Authors: R. J. Daigle and C. D. Feustel
Journal: Proc. Amer. Math. Soc. 45 (1974), 441-444
MSC: Primary 57A10; Secondary 57C35
DOI: https://doi.org/10.1090/S0002-9939-1974-0383410-5
MathSciNet review: 0383410
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we give an example which shows that the existence of an essential map of an annulus in a nonorientable $ 3$-manifold does not guarantee the existence of an essential embedding in that manifold.


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

  • [1] E. M. Brown and R. H. Crowell, Deformation retractions of $ 3$-manifolds into their boundaries, Ann. of Math. (2) 82 (1965), 445-458. MR 31 #6236. MR 0182012 (31:6236)
  • [2] C. D. Feustel, On embedding essential annuli in $ {M^3}$, Canad. J. Math. (to appear). MR 0362311 (50:14753)
  • [3] F. Waldhausen, On irreducible $ 3$-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56-88. MR 36 #7146. MR 0224099 (36:7146)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0383410-5
Keywords: Essential map, essential embedding
Article copyright: © Copyright 1974 American Mathematical Society

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