Generalized Seifert surfaces and signatures of colored links

Details Generalized Seifert surfaces and signatures of colored links Generalized Seifert surfaces and signatures of colored links

2005-05-10

arxiv.org/abs/math/0505185v2

Mathematics

Geometric Topology

40 pages, 20 figures

Scientific paper

In this paper, we use `generalized Seifert surfaces' to extend the Levine-Tristram signature to colored links in S^3. This yields an integral valued function on the m-dimensional torus, where m is the number of colors of the link. The case m=1 corresponds to the Levine-Tristram signature. We show that many remarkable properties of the latter invariant extend to this m-variable generalization: it vanishes for achiral colored links, it is `piecewise continuous', and the places of the jumps are determined by the Alexander invariants of the colored link. Using a 4-dimensional interpretation and the Atiyah-Singer G-signature theorem, we also prove that this signature is invariant by colored concordance, and that it provides a lower bound for the `slice genus' of the colored link.

Affiliated with

Also associated with

No associations

Rating

Generalized Seifert surfaces and signatures of colored links 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 Generalized Seifert surfaces and signatures of colored links, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Seifert surfaces and signatures of colored links will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-312956