Recognizing trivial links in polynomial time

Details Recognizing trivial links in polynomial time Recognizing trivial links in polynomial time

2011-10-13

arxiv.org/abs/1110.2871v1

Mathematics

Geometric Topology

74 pages, 58 figures. TeX file contains all Tikz source necessary to generate figures

Scientific paper

Trivial links are unique up to number of link components, but they can be hard to recognize from arbitrary diagrams. We define a measure, the crumple, on link diagrams and then demonstrate that for trivial links there is a sequence of moves by which the crumple may be strictly monotonically reduced. By our definition, the minimum possible crumple over all link diagrams is achieved only by embedding components disjointly in parallel planes, and so a link will be able to obtain this crumple if and only if it is trivial. The crumple is quadratic in the number of crossings, and we show that finding each reducing move takes only polynomial time and linear space. Therefore, we may decide whether a link is trivial in time polynomial on the number of crossings of a diagram of the link.

Affiliated with

Also associated with

No associations

Rating

Recognizing trivial links in polynomial time 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 Recognizing trivial links in polynomial time, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recognizing trivial links in polynomial time will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-499976