On region crossing change and incidence matrix

Details On region crossing change and incidence matrix On region crossing change and incidence matrix

2011-01-06

arxiv.org/abs/1101.1129v2

Mathematics

Geometric Topology

10 pages, 7 figures

Scientific paper

In a recent work of Ayaka Shimizu$^{[5]}$, she defined an operation named region crossing change on link diagrams, and showed that region crossing change is an unknotting operation for knot diagrams. In this paper, we prove that region crossing change on a 2-component link diagram is an unknotting operation if and only if the linking number of the diagram is even. Besides, we define an incidence matrix of a link diagram via its signed planar graph and its dual graph. By studying the relation between region crossing change and incidence matrix, we prove that a signed planar graph represents an $n$-component link diagram if and only if the rank of the associated incidence matrix equals to $c-n+1$, here $c$ denotes the size of the graph.

Affiliated with

Also associated with

No associations

Rating

On region crossing change and incidence matrix 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 On region crossing change and incidence matrix, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On region crossing change and incidence matrix will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-398536