Extending Isotopies of Planar Continua

Details Extending Isotopies of Planar Continua Extending Isotopies of Planar Continua

2008-11-03

arxiv.org/abs/0811.0364v1

Mathematics

Geometric Topology

23 pages, 1 figure

Scientific paper

In this paper we solve the following problem in the affirmative: Let $Z$ be a continuum in the plane $\complex$ and suppose that $h:Z\times [0,1]\to\complex$ is an isotopy starting at the identity. Can $h$ be extended to an isotopy of the plane? We will provide a new characterization of an accessible point in a planar continuum $Z$ and use it to show that an accessible point is preserved during the isotopy. We show next that the isotopy can be extended over hyperbolic crosscuts. The proof makes use of the notion of a metric external ray, which mimics the notion of a conformal external ray, but is easier to control during an isotopy.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-234423