Cyclic surgery theorem

Cyclic surgery theorem

In three-dimensional topology, a branch of mathematics, the cyclic surgery theorem states that, for a compact, connected, orientable, irreducible three-manifold M whose boundary is a torus T, if M is not a Seifert-fibered space and r,s are slopes on T such that their Dehn fillings have cyclic fundamental group, then the distance between r and s (the minimal number of times that two simple closed curves in T representing r and s must intersect) is at most 1. Consequently, there are at most three Dehn fillings of M with cyclic fundamental group. The theorem appeared in a 1987 paper written by Marc Culler, Cameron Gordon, John Luecke and Peter Shalen.[1]

References

  1. ^ M. Culler, C. Gordon, J. Luecke, P. Shalen (1987). Dehn surgery on knots. The Annals of Mathematics (Annals of Mathematics) 125 (2): 237-300.

Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Gordon-Luecke theorem — In mathematics, the Gordon Luecke theorem on knot complements states that every homeomorphism between two complements of knots in the 3 sphere extends to give a self homeomorphism of the 3 sphere. In other words, any homeomorphism between knot… …   Wikipedia

  • Gordon–Luecke theorem — In mathematics, the Gordon–Luecke theorem on knot complements states that every homeomorphism between two complements of knots in the 3 sphere extends to give a self homeomorphism of the 3 sphere. In other words, any homeomorphism between knot… …   Wikipedia

  • Marc Culler — Photograph by Roberta Devlin Born November 22, 1953 …   Wikipedia

  • 3-manifold — In mathematics, a 3 manifold is a 3 dimensional manifold. The topological, piecewise linear, and smooth categories are all equivalent in three dimensions, so little distinction is usually made in whether we are dealing with say, topological 3… …   Wikipedia

  • Peter Shalen — Peter B. Shalen is an American mathematician, working primarily in low dimensional topology. He is the S in JSJ decomposition. LifeHe graduated from Stuyvesant High School in 1962, [cite web |url=http://65.104.11.121/MathTeam.html… …   Wikipedia

  • Cameron Gordon (mathematician) — Cameron Gordon is a professor of mathematics at the University of Texas at Austin, known for his work in knot theory. Among his notable results is his work with Marc Culler, John Luecke, and Peter Shalen on the cyclic surgery theorem. This was an …   Wikipedia

  • Small cancellation theory — In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have small overlaps with each other. It turns out that… …   Wikipedia

  • Geometrization conjecture — Thurston s geometrization conjecture states that compact 3 manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3 manifolds of the uniformization theorem for… …   Wikipedia

  • Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   Wikipedia

  • Exotic sphere — In differential topology, a mathematical discipline, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n sphere. That is, M is a sphere from the point of view of all its… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”