A Proof of the Melvin{morton Conjecture and Feynman Diagrams

نویسنده

  • S. CHMUTOV
چکیده

The Melvin{Morton conjecture says how the Alexander{Conway knot invariant function can be read from the coloured Jones function. It has been proved by D. Bar-Natan and S. Garoufalidis. They reduced the conjecture to a statement about weight systems. The proof of the latter is the most diicult part of their paper. We give a new proof of the statement based on the Feynman diagram description of the primitive space of the Hopf algebra A of chord diagrams.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Partial proof of Graham Higman's conjecture related to coset diagrams

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

متن کامل

PROOF OF A CONJECTURE OF KULAKOVA ET AL. RELATED TO THE sl2 WEIGHT SYSTEM

In this article, we show that a conjecture raised in [KLMR], which regards the coefficient of the highest term when we evaluate the sl2 weight system on the projection of a diagram to primitive elements, is equivalent to the Melvin-Morton-Rozansky conjecture, proven in [BG].

متن کامل

Random Walk on Knot Diagrams, Colored Jones Polynomial and Ihara-selberg Zeta Function

A model of random walk on knot diagrams is used to study the Alexander polynomial and the colored Jones polynomial of knots. In this context, the inverse of the Alexander polynomial of a knot plays the role of an Ihara-Selberg zeta function of a directed weighted graph, counting with weights cycles of random walk on a 1-string link whose closure is the knot in question. The colored Jones polyno...

متن کامل

A short proof of the maximum conjecture in CR dimension one

In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...

متن کامل

Proof of a conjecture of Kulakova et al. related to the s12 weight system

In this article, we show that a conjecture raised in [KLMR], which regards the coefficient of the highest term when we evaluate the sl2 weight system on the projection of a diagram to primitive elements, is equivalent to the Melvin-Morton-Rozansky conjecture, proven in [BG].

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007