Mathematics – Geometric Topology
Scientific paper
2007-06-13
J. Knot Theory Ramifications 18(8):1129-1157 (2009)
Mathematics
Geometric Topology
25 pages, 5 figures, to appear in JKTR. v3: example of the target groups added; slight correction to the construction of the t
Scientific paper
10.1142/S0218216509007385
Given a knot K we may construct a group G_n(K) from the fundamental group of K by adjoining an nth root of the meridian that commutes with the corresponding longitude. These "generalised knot groups" were introduced independently by Wada and Kelly, and contain the fundamental group as a subgroup. The square knot SK and the granny knot GK are a well known example of a pair of distinct knots with isomorphic fundamental groups. We show that G_n(SK) and G_n(GK) are non-isomorphic for all n>1. This confirms a conjecture of Lin and Nelson, and shows that the isomorphism type of G_n(K), n>1, carries more information about K than the isomorphism type of the fundamental group. An appendix by David Savitt contains some results on representations of the trefoil group in PSL(2,p) that are needed for the proof.
No associations
LandOfFree
Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt) 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 Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-450449