A proof of Tait's Conjecture on alternating-achiral knots

Details A proof of Tait's Conjecture on alternating-achiral knots A proof of Tait's Conjecture on alternating-achiral knots

2011-03-16

arxiv.org/abs/1103.3203v1

Mathematics

Geometric Topology

23 pages, 20 figures

Scientific paper

In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait's Conjecture on alternating -achiral knots: Let K be an alternating -achiral knot. Then there exists a minimal projection {\Pi} of K in S^2 \subset S^3 and an involution {\phi}:S^3\toS^3 such that: 1) {\phi} reverses the orientation of $S^3$; 2) {\phi}(S^2) = S^2; 3) {\phi} ({\Pi}) = {\Pi}; 4) {\phi} has two fixed points on {\Pi} and hence reverses the orientation of K. The purpose of this paper is to prove this statement.

Affiliated with

Also associated with

No associations

Rating

A proof of Tait's Conjecture on alternating-achiral knots 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 A proof of Tait's Conjecture on alternating-achiral knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A proof of Tait's Conjecture on alternating-achiral knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-263491