Planar and spherical stick indices of knots

Details Planar and spherical stick indices of knots Planar and spherical stick indices of knots

2011-08-29

arxiv.org/abs/1108.5700v1

Journal of Knot Theory and its Ramifications, Vol. 20, Issue 5, 721-739 (2011)

Mathematics

Geometric Topology

Scientific paper

10.1142/S0218216511008954

The stick index of a knot is the least number of line segments required to build the knot in space. We define two analogous 2-dimensional invariants, the planar stick index, which is the least number of line segments in the plane to build a projection, and the spherical stick index, which is the least number of great circle arcs to build a projection on the sphere. We find bounds on these quantities in terms of other knot invariants, and give planar stick and spherical stick constructions for torus knots and for compositions of trefoils. In particular, unlike most knot invariants,we show that the spherical stick index distinguishes between the granny and square knots, and that composing a nontrivial knot with a second nontrivial knot need not increase its spherical stick index.

Affiliated with

Also associated with

No associations

Rating

Planar and spherical stick indices of 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 Planar and spherical stick indices of knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Planar and spherical stick indices of knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127295