TORUS KNOTS AND 3-MANIFOLDS
Authors:
- 1 December 2004
- journal article
- Published by World Scientific Pub Co Pte Ltd in Journal of Knot Theory and Its Ramifications
- Vol. 13 (08) , 1103-1119
Abstract
We consider a family of words in a free group of rank n which determine 3-manifolds ℳn(p,q). We prove that the fundamental groups of ℳn(p,q) are cyclically presented, and that ℳn(p,q) is the n-fold cyclic covering of the 3-sphere branched over the torus knots T(p,q) if p is odd and q≡±2( mod p). We also obtain an explicit Dunwoody parameters for the torus knots T(p,q) for odd p and q≡±2( mod p).Keywords
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