Constructing knot tunnels using giant steps

Details Constructing knot tunnels using giant steps Constructing knot tunnels using giant steps

2008-12-07

arxiv.org/abs/0812.1382v1

Mathematics

Geometric Topology

10 pages, 5 figures

Scientific paper

This is the first of three papers that refine and extend portions of our earlier preprint, "Depth of a knot tunnel." Together, they rework the entire preprint. H. Goda, M. Scharlemann, and A. Thompson described a general construction of all tunnels of all tunnel number 1 knots using "tunnel moves". We apply the theory that we introduced in "The tree of knot tunnels" to study this construction. In particular, we use it to calculate the number of distinct minimal sequences of tunnel moves that can produce a given tunnel. As a consequence, we see that for a sparse infinite set of tunnels, the minimal sequence is unique, but generically a tunnel will have many such constructions.

Affiliated with

Also associated with

No associations

Rating

Constructing knot tunnels using giant steps 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 Constructing knot tunnels using giant steps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing knot tunnels using giant steps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-450289