18 Conjectures
Abstract.
I will state 18=3x3x2 "fundamental" conjectures on finite type invariants of
various classes of virtual knots. This done, I will state a few further
conjectures about these conjectures and ask a few questions about how these 18
conjectures may or may not interact.
See also Some Dimensions of
Spaces of Finite Type Invariants of Virtual Knots, with Halacheva,
Leung, and Roukema. |
w-Knots, from Z to A
Abstract.
I will define w-knots, a class of knots wider than ordinary knots
but weaker than virtual knots, and show that it is quite easy to
construct a universal finite invariant Z of w-knots. In order
to study Z we will introduce the "Euler Operator" and the
"Infinitesimal Alexander Module", at the end finding a simple determinant
formula for Z. With no doubt that formula computes the Alexander
polynomial A, except I don't have a proof yet.
See also Finite Type Invariants of
w-Knotted Objects: From Alexander to Kashiwara and Vergne. |