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*{{citation|first=L.|last=Antoine|title=Sur la possibilité d'étendre l'homéomorphie de deux figures à leurs voisinages|journal=C. R. Acad. Sci. Paris|year=1920|volume=171|page=661}} |
*{{citation|first=L.|last=Antoine|title=Sur la possibilité d'étendre l'homéomorphie de deux figures à leurs voisinages|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]] | mr=0140096 | year=1962 | chapter=The Wilder arcs | pages=184–187}} |
*{{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]] | mr=0140096 | year=1962 | chapter=The Wilder arcs | pages=184–187}} |
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*{{Citation | last1=Fox | first1=Ralph H. |author1-link=Ralph Fox| last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | jstor=1969408 | mr=0027512 | year=1948 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=49 | pages=979–990 | doi=10.2307/1969408}} |
*{{Citation | last1=Fox | first1=Ralph H. |author1-link=Ralph Fox| last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | jstor=1969408 | mr=0027512 | year=1948 | journal=[[Annals of Mathematics]] |series=Second Series | issn=0003-486X | volume=49 | issue=4 | pages=979–990 | doi=10.2307/1969408}} |
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* {{cite book |
* {{cite book|first1=John Gilbert|last1=Hocking|first2=Gail Sellers|last2=Young|title=Topology|year=1988|orig-year=1961|publisher=Dover|isbn=0-486-65676-4|pages=[https://archive.org/details/topology00hock_0/page/176 176–177]|url-access=registration|url=https://archive.org/details/topology00hock_0/page/176}} |
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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 | mr=0343276 | year=1973 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=45 | pages=585–598 | doi=10.2140/pjm.1973.45.585| doi-access=free }} |
*{{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 | mr=0343276 | year=1973 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=45 | issue=2 | pages=585–598 | doi=10.2140/pjm.1973.45.585| doi-access=free }} |
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[[Category:Geometric topology]] |
[[Category:Geometric topology]] |
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Revision as of 00:31, 19 February 2021
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In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an ambient isotopy taking the arc to a straight line segment. Antoine (1920) found the first example of a wild arc, and Fox & Artin (1948) found another example called the Fox–Artin arc whose complement is not simply connected.
See also
Further reading
- Antoine, L. (1920), "Sur la possibilité d'étendre l'homéomorphie de deux figures à leurs voisinages", C. R. Acad. Sci. Paris, 171: 661
- 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, MR 0140096
- Fox, Ralph H.; Artin, Emil (1948), "Some wild cells and spheres in three-dimensional space", Annals of Mathematics, Second Series, 49 (4): 979–990, doi:10.2307/1969408, ISSN 0003-486X, JSTOR 1969408, MR 0027512
- Hocking, John Gilbert; Young, Gail Sellers (1988) [1961]. Topology. Dover. pp. 176–177. ISBN 0-486-65676-4.
- McPherson, James M. (1973), "Wild arcs in three-space. I. Families of Fox–Artin arcs", Pacific Journal of Mathematics, 45 (2): 585–598, doi:10.2140/pjm.1973.45.585, ISSN 0030-8730, MR 0343276