© | << < ? > >> | Dror Bar-Natan: Talks: | Links: Demo GGAD GPV KBH WKO1 WKO2 WKO4 |

**Abstract.** In a "degree $d$ Gauss diagram formula" one produces
a number by summing over all possibilities of paying very close attention
to $d$ crossings in some $n$-crossing knot diagram while observing the
rest of the diagram only very loosely, minding only its skeleton. The
result is always poly-time computable as only $\binom{n}{d}$ states
need to be considered. An under-explained paper by Goussarov, Polyak,
and Viro [GPV] shows that every type $d$ knot invariant
has a formula of this kind. Yet only finitely many integer invariants
can be computed in this manner within any specific polynomial time bound.

I suggest to do the same as [GPV], except replacing "the skeleton" with "the Gassner invariant", which is still poly-time. One poly-time invariant that arises in this way is the Alexander polynomial (in itself it is infinitely many numerical invariants) and I believe (and have evidence to support my belief) that there are more.

**Handout:**
GG.html,
GG.pdf,
GG.png.

**Proposal:** Summary.pdf, Detailed.pdf.

**Sources:** pensieve.