The Alexander polynomial of (1,1)-knots

Details The Alexander polynomial of (1,1)-knots The Alexander polynomial of (1,1)-knots

2005-01-23

arxiv.org/abs/math/0501394v2

Mathematics

Geometric Topology

11 pages, 1 figure. A corollary has been extended, and a new example added. Accepted for publication on J. Knot Theory Ramific

Scientific paper

In this paper we investigate the Alexander polynomial of (1,1)-knots, which are knots lying in a 3-manifold with genus one at most, admitting a particular decomposition. More precisely, we study the connections between the Alexander polynomial and a polynomial associated to a cyclic presentation of the fundamental group of an n-fold strongly-cyclic covering branched over the knot, which we call the n-cyclic polynomial. In this way, we generalize to all (1,1)-knots, with the only exception of those lying in S^2\times S^1, a result obtained by J. Minkus for 2-bridge knots and extended by the author and M. Mulazzani to the case of (1,1)-knots in the 3-sphere. As corollaries some properties of the Alexander polynomial of knots in the 3-sphere are extended to the case of (1,1)-knots in lens spaces.

Affiliated with

Also associated with

No associations

Rating

The Alexander polynomial of (1,1)-knots does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Alexander polynomial of (1,1)-knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Alexander polynomial of (1,1)-knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-473456