Ordered groups, eigenvalues, knots, surgery and L-spaces

Details Ordered groups, eigenvalues, knots, surgery and L-spaces Ordered groups, eigenvalues, knots, surgery and L-spaces

2010-04-21

arxiv.org/abs/1004.3615v2

Mathematics

Algebraic Topology

Minor changes from first version

Scientific paper

We establish a necessary condition that an automorphism of a nontrivial finitely generated bi-orderable group can preserve a bi-ordering: at least one of its eigenvalues, suitably defined, must be real and positive. Applications are given to knot theory, spaces which fibre over the circle and to the Heegaard-Floer homology of surgery manifolds. In particular, we show that if a nontrivial fibred knot has bi-orderable knot group, then its Alexander polynomial has a positive real root. This implies that many specific knot groups are not bi-orderable. We also show that if the group of a nontrivial knot is bi-orderable, surgery on the knot cannot produce an $L$-space, as defined by Ozsv\'ath and Szab\'o.

Affiliated with

Also associated with

No associations

Rating

Ordered groups, eigenvalues, knots, surgery and L-spaces 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 Ordered groups, eigenvalues, knots, surgery and L-spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ordered groups, eigenvalues, knots, surgery and L-spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-326196