Pacific Journal of Mathematics

Wild arcs in three-space. I. Families of Fox-Artin arcs.

James M. McPherson

Article information

Source
Pacific J. Math. Volume 45, Number 2 (1973), 585-598.

Dates
First available: 13 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102947540

Zentralblatt MATH identifier
0253.55002

Zentralblatt MATH identifier
0221.55003

Mathematical Reviews number (MathSciNet)
MR0343276

Subjects
Primary: 57A10
Secondary: 55A30

Citation

McPherson, James M. Wild arcs in three-space. I. Families of Fox-Artin arcs. Pacific Journal of Mathematics 45 (1973), no. 2, 585--598. http://projecteuclid.org/euclid.pjm/1102947540.


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References

  • [1] W. R.Alford andB.J. Ball, Some almost polyhedral wild arcs, Duke Math. J., 30 (1963), 33-38.
  • [2] R.H.Fox, Some problems in knot theory, in TOPOLOGY OF3-MANIFOLDS,ed. M. K. Fort, Jr., Prentice Hall, Englewood Cliffs, N.J. 1962.
  • [3] R.H.FoxandE. Artin, Some wild cells and spheres in three-dimensionalspace, Ann. Math., (2)49 (1948), 979-990.
  • [4] R.H.Foxand0. G.Harrold, TheWilder arcs, inTOPOLOGY OF3-MANIFOLDS, ed. M. K. Fort, Jr., Prentice Hall, Englewood Cliffs, N.J. 1962.
  • [5] C.H.Giffen, Uncountably many inequivalent nearly tame arcs, Abstract 607-19, Notices Amer. Math. Math. Soc,10 (1963), 666-667.
  • [6] Y. Hashizume, Onthe uniqueness of the decomposition of a link, Osaka Math. J.,
  • [7] R. Holmes and N. Smythe, Algebraic invariants of isotopy of links, Amer. J. Math., 88 (1966), 646-654.
  • [8] S. J. Lomonaco, An algebraic theory of local knottedness, I, Trans. Amer. Math. Soc. 129 (1967), 322-343.
  • [9] J. McPherson, Wild knots and arcs in a ^-manifold,University of New South Wales Ph. D. thesis, 1970.
  • [10] J. McPherson, A sufficient condition for an arc to be nearly polyhedral, Proc. Amer. Math. Soc, 28 (1971), 229-233. 11.1A familyof non-invertibleprime links, Bull. Austral. Math. Soc, 4 (1971), 105-108, Corrigendum 5 (1971), 141-143.
  • [12] C. D. Sikkema, A duality between certain spheres and arcs in S3, Trans. Amer. Math. Soc, 122 (1966), 399-415.
  • [13] C. D. Sikkema, S. Kinoshita, and S. J. Lomonaco, Uncountably manyquasi-trans- lations of Sz, manuscript.
  • [14] N. Smythe, Topological invariants of isotopy of links, I, Amer. J. Math., 92 (1970), 86-98.

See also

  • II : James M. McPherson. Wild arcs in three-space. II. An invariant of non-oriented local type. Pacific Journal of Mathematics volume 44, issue 2, (1973), pp. 619-636.
  • III : James M. McPherson. Wild arcs in three-space. III. An invariant of oriented local type for exceptional arcs. Pacific Journal of Mathematics volume 45, issue 2, (1973), pp. 599-620.