Travel prevented by the homeopathic ash cloud, talk given in Goettingen, instead

Talk in Luminy, April 2010

Algebraic and Quantum Topology
(in honour of Pierre Vogel)
April 19 - 23

I will give the talk on the left and the talk on the right will be on the back side of the handout.

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.

Handout. 18C.html, 18C.pdf. Talk Video (in Goettingen).

Handout. Z2A.html, Z2A.pdf. Talk Video: Part I, Part II (in Toronto).