The concordance genus of knots

Details The concordance genus of knots The concordance genus of knots

2001-07-19

arxiv.org/abs/math/0107141v2

Algebr. Geom. Topol. 4 (2004) 1-22

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-1.abs.html

Scientific paper

In knot concordance three genera arise naturally, g(K), g_4(K), and g_c(K): these are the classical genus, the 4-ball genus, and the concordance genus, defined to be the minimum genus among all knots concordant to K. Clearly 0 <= g_4(K) <= g_c(K) <= g(K). Casson and Nakanishi gave examples to show that g_4(K) need not equal g_c(K). We begin by reviewing and extending their results. For knots representing elements in A, the concordance group of algebraically slice knots, the relationships between these genera are less clear. Casson and Gordon's result that A is nontrivial implies that g_4(K) can be nonzero for knots in A. Gilmer proved that g_4(K) can be arbitrarily large for knots in A. We will prove that there are knots K in A with g_4(K) = 1 and g_c(K) arbitrarily large. Finally, we tabulate g_c for all prime knots with 10 crossings and, with two exceptions, all prime knots with fewer than 10 crossings. This requires the description of previously unnoticed concordances.

Affiliated with

Also associated with

No associations

Rating

The concordance genus of 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 The concordance genus of knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The concordance genus of knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-282950