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Antoine's Horned Sphere

A topological 2-sphere in 3-space whose exterior is not Simply Connected. The outer complement of Antoine's horned sphere is not Simply Connected. Furthermore, the group of the outer complement is not even finitely generated. Antoine's horned sphere is inequivalent to Alexander's Horned Sphere since the complement in $\Bbb{R}^3$ of the bad points for Alexander's Horned Sphere is Simply Connected.

See also Alexander's Horned Sphere


Alexander, J. W. ``An Example of a Simply-Connected Surface Bounding a Region which is not Simply-Connected.'' Proc. Nat. Acad. Sci. 10, 8-10, 1924.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 76-79, 1976.

© 1996-9 Eric W. Weisstein