Knot theory for self-indexed graphs

Details Knot theory for self-indexed graphs Knot theory for self-indexed graphs

2003-04-04

arxiv.org/abs/math/0304061v1

Mathematics

Geometric Topology

14 pages

Scientific paper

We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure, an integral flow. We call a self-indexed graph with integral flow a comte. The analogy with links allows us to define transformations of comtes generalizing the Reidemeister moves on link diagrams. We show that many invariants of links can be generalized to comtes, most notably the linking number, the Alexander polynomials, the link group, etc. We also discuss finite type invariants and quandle cocycle invariants of comtes.

Affiliated with

Also associated with

No associations

Rating

Knot theory for self-indexed graphs 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 Knot theory for self-indexed graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Knot theory for self-indexed graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-385449