Download or read book Two-Bridge Knots Have Property $\mathbf {P}$ written by Moto-o Takahashi and published by American Mathematical Soc.. This book was released on 1981 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: A knot K is said to have Property P if simply-connected 3-manifolds cannot be obtained by non-trivial Dehn surgeries along K. Torus knots, twist knots, a class of 2-bridge knots, and 2-bridge knots with 9 or fewer crossings are known to have Property P. On the other hand, Ochiai proves that the 3-sphere cannot be obtained by a non-trivial surgery along a two-bridge knot. In this monograph we shall prove that every non-trivial two-bridge knot has Property P. In the proof we shall use Bezout's theorem in algebraic geometry.