The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces

Details The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces

2002-09-03

arxiv.org/abs/math/0209027v2

Algebr. Geom. Topol. 3 (2003) 89-101

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-3.abs.html

Scientific paper

It is well-known that self-linking is the only Z valued Vassiliev invariant of framed knots in S^3. However for most 3-manifolds, in particular for the total spaces of S^1-bundles over an orientable surface F not S^2, the space of Z-valued order one invariants is infinite dimensional. We give an explicit formula for the order one invariant I of framed knots in orientable total spaces of S^1-bundles over an orientable not necessarily compact surface F not S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order one invariant, i.e. it distinguishes every two framed knots that can be distinguished by order one invariants with values in an Abelian group.

Affiliated with

Also associated with

No associations

Rating

The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces 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 universal order one invariant of framed knots in most S^1-bundles over orientable surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The universal order one invariant of framed knots in most S^1-bundles over orientable surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-76914