The head and tail conjecture for alternating knots

We investigate the coefficients of the highest and lowest terms (also called the head and the tail) of the colored Jones polynomial and show that they stabilize for alternating links and for adequate links. To do this we apply techniques from skein theory

A reduced set of moves on one-vertex ribbon graphs coming from links

Every link in R^3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams.Comment: 14 pages, 15 figure

A Reduced Set of Moves on One-Vertex Ribbon Graphs Coming from Links

Every link in R3 can be represented by a one-vertex ribbon graph. We prove a Markov type theorem on this subset of link diagrams

The head and tail of the Colored Jones polynomial for adequate knots

We show that the head and tail functions of the colored Jones polynomial of adequate links are the product of head and tail functions of the colored Jones polynomial of alternating links that can be read-off an adequate diagram of the link. We apply this to strengthen a theorem of Kalfagianni, Futer and Purcell on the fiberedness of adequate links