Global knot theory in F^2 x R
Abstract
We introduce a special class of knots, called global knots, in F^2 x R and we construct new isotopy invariants, called Tinvariants, for global knots. Some Tinvariants are of finite type but they cannot be extracted from the generalized Kontsevitch integral (which is consequently not the universal invariant of finite type for the restricted class of global knots). We prove that Tinvariants separate all global knots of a certain type. As a corollary, we prove the noninvertibility of some links in S^3 without making any use of the link group.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012087
 Bibcode:
 2000math.....12087F
 Keywords:

 Geometric Topology
 EPrint:
 75 pages, 79 figures