Pacific Journal of Mathematics

Indecomposable surfaces in $4$-space.

Charles Livingston

Article information

Pacific J. Math., Volume 132, Number 2 (1988), 371-378.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations 20J05: Homological methods in group theory 57M99: None of the above, but in this section


Livingston, Charles. Indecomposable surfaces in $4$-space. Pacific J. Math. 132 (1988), no. 2, 371--378.

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  • [A] K. Asano, A note on surfaces in 4-space, Math. Seminar Notes, Kobe Univer- sity, 4 (1976), 195-198.
  • [Art] E. Artin, Zur Isotopie zweidimensionaler Flachen in R4, Abh. Mathe. Seminar Univ. Hamburg, 4 (1925), 174-177.
  • [B] K. Brown, Cohomology of Groups, New York, Springer-Verlag, 1982.
  • [BMS] A. M. Brunner, E. J. Mayland, and J. Simon, Knot groups in S4 with nontrivial homology, Pacific J. Math., 103 (1982), 315-321.
  • [F] C. D. Feustel, A generalization of Kneser's conjecture, Pacific J. Math., 46 (1973), 123-130.
  • [G] C. McA. Gordon, Homology groups of surfaces in the 4-sphere, Math. Proc. Camb. Phil. Soc, 89 (1981), 113-117.
  • [Lith] R. A. Litherland, The second homology of the group of a knotted surface, Quar. J. Math. Oxford (2), 32 (1981), 425-434.
  • [L] C. Livingston, Stably irreducible surfaces in S4, Pacific J. Math., 116 (1985), 77-84.
  • [M] T. Maeda, On the groups with Wirtinger presentations, Math. Seminar Notes, Kwansei Gakuin Univ. 1977.
  • [MKS] W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, Dover Publications, Inc., New York, 1976.
  • [PR] T. Price and D. Roseman, Some examples of projectiveplanes and twospheres in 4-space, preprint.
  • [SW] P. Scott and C. T. C. Wall, Topological methods in group theory, Homological Group Theory, ed. C. T. C. Wall, New York, Cambridge University Press, 1979.