##
Michael Polyak

Department of Mathematics Technion - Israel
Institute of Technology

Quadrisecants, homology intersections and finite
type invariants.

### Résumé

Suppose that we managed to assign some signs to quadrisecants of a
knot (i.e., lines cutting it 4 points) so that their total number, counted with
signs, does not change under knot isotopy. What kind of invariant is it, and
how to assign such signs? While the answer in this case is known, it motivates
more general attempts to count (with signs) various geometric objects inscribed
into a knot or a plane curve. In all cases invariants are easily seen to be of
finite type. I will explain a general setting to produce such invariants (using
evaluation maps of configuration spaces and homology intersections) and will
formulate some results and conjectures.
No prior knowledge of these themes will be assumed.