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A new approach to knot theory


Speaker: Thomas Fiedler, MSRI
Location: 693 Kerr
Start time: Wed, Apr 14 2004, 4:10PM

One associates to a knot in the solid torus ( e.g. a knot in 3-space or a closed braid ) a singular link , called trace link , in a thickened torus . The trace link is well defined up to some combinatorial equivalence relation and it is a complete knot invariant .First one derives numerical invariants from the trace link . But at least in the case of closed braids one can do even better . One brings the trace link into a set of normal forms which is of polynomial size .