On standard forms of 1--dominations between knots with same Gromov volumes

Details On standard forms of 1--dominations between knots with same Gromov volumes On standard forms of 1--dominations between knots with same Gromov volumes

2008-01-13

arxiv.org/abs/0801.1943v1

Mathematics

Geometric Topology

15 pages

Scientific paper

Let $k$ and $k'$ be two knots in 3-sphere. Say $k$ 1--dominates $k'$, if there is a proper degree 1 map $f\co E(k)\to E(k')$, between knot exterior of $k_i$. Theorem: Suppose that any companion of $k$ is prime. If $k$ 1--dominates $k'$ with the same Gromov volume, then $k'$ can be obtained from $k$ by finitely many de-satellizations. The condition of "same Gromov volume" clearly can not be removed. We also give a new construction of 1-domination between knots with same Gromov volume to show that the condition "any companion of $k$ is prime" can not be removed.

Affiliated with

Also associated with

No associations

Rating

On standard forms of 1--dominations between knots with same Gromov volumes 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 standard forms of 1--dominations between knots with same Gromov volumes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On standard forms of 1--dominations between knots with same Gromov volumes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-472732