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4:00 pm Monday, November 7, 2011 Topology Seminar: On the injectivity of satellite operations in knot concordanceby Tim Cochran (Rice University) in HB 427- Satellite operations may be viewed as functions from the set of knot types to the set of knot types. It is not hard to see, using standard tools of 3-manifolds, that these functions are injective. It is well known that these functions descend to give operators (not homomorphisms) on the group of concordance classes of knots. It is conjectured that many of these are also injective. The Whitehead Double operator is the most famous. We will prove that for a very large class of operators, P, modulo the smooth 4-d poincare conjecture, P(K)=P(Unknot) implies K=Unknot.
Submitted by cochran@rice.edu |