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==References== |
==References== |
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*{{citation|first=L.|last=Antoine|journal=C.R. Acad. Sci. Paris|year=1920|volume=171|page=661}} |
*{{citation|first=L.|last=Antoine|journal=C.R. Acad. Sci. Paris|year=1920|volume=171|page=661}} |
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*{{Citation | last1=Fox | first1=Ralph H. | last2=Harrold | first2=O. G. | title=Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) | publisher=[[Prentice Hall]] | id={{MathSciNet | id = 0140096}} | year=1962 | chapter=The Wilder arcs | pages=184–187}} |
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*{{Citation | last1=Fox | first1=Ralph H. | last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | url=http://www.jstor.org/stable/1969408 | id={{MathSciNet | id = 0027512}} | year=1948 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=49 | pages=979–990}} |
*{{Citation | last1=Fox | first1=Ralph H. | last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | url=http://www.jstor.org/stable/1969408 | id={{MathSciNet | id = 0027512}} | year=1948 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=49 | pages=979–990}} |
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*{{Citation | last1=McPherson | first1=James M. | title=Wild arcs in three-space. I. Families of Fox-Artin arcs | url=http://projecteuclid.org/euclid.pjm/1102947540 | id={{MathSciNet | id = 0343276}} | year=1973 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=45 | pages=585–598}} |
*{{Citation | last1=McPherson | first1=James M. | title=Wild arcs in three-space. I. Families of Fox-Artin arcs | url=http://projecteuclid.org/euclid.pjm/1102947540 | id={{MathSciNet | id = 0343276}} | year=1973 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=45 | pages=585–598}} |
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Revision as of 17:37, 18 January 2010
In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one. Antoine (1920) found the first example, and Fox & Artin (1948) found an example called the Fox-Artin arc whose complement is simply connected.
References
- Antoine, L. (1920), C.R. Acad. Sci. Paris, 171: 661
{{citation}}: Missing or empty|title=(help) - Fox, Ralph H.; Harrold, O. G. (1962), "The Wilder arcs", Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961), Prentice Hall, pp. 184–187, MR0140096
- Fox, Ralph H.; Artin, Emil (1948), "Some wild cells and spheres in three-dimensional space", Annals of Mathematics. Second Series, 49: 979–990, ISSN 0003-486X, MR0027512
- McPherson, James M. (1973), "Wild arcs in three-space. I. Families of Fox-Artin arcs", Pacific Journal of Mathematics, 45: 585–598, ISSN 0030-8730, MR0343276