Infinite family of non-concordant knots having the same Seifert form

Details Infinite family of non-concordant knots having the same Seifert form Infinite family of non-concordant knots having the same Seifert form

2004-02-26

arxiv.org/abs/math/0402425v1

Mathematics

Geometric Topology

7 pages

Scientific paper

By a recent result of Livingston, it is known that if a knot has a prime power branched cyclic cover that is not a homology sphere, then there is an infinite family of non-concordant knots having the same Seifert form as the knot. In this paper, we extend this result to the full extent. We show that if the knot has nontrivial Alexander polynomial, then there exists an infinite family of non-concordant knots having the same Seifert form as the knot. As a corollary, no nontrivial Alexander polynomial determines a unique knot concordance class. We use Cochran-Orr-Teichner's recent result on the knot concordance group and Cheeger-Gromov's von Neumann rho invariants with their universal bound for a 3-manifold.

Affiliated with

Also associated with

No associations

Rating

Infinite family of non-concordant knots having the same Seifert form 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 Infinite family of non-concordant knots having the same Seifert form, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Infinite family of non-concordant knots having the same Seifert form will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-130388