分野別セミナー

A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are placed on the bottom, and every link can be represented as the closure of a bottom tangle. We study the universal $sl_2$ invariant of three types of bottom tangle which are called boundary, ribbon, and brunnian. For each type of bottom tangle, we give a certain small subalgebra in which the universal $sl_2$ invariant of the type of bottom tangle takes values. Those results are applied to the colored Jones polynomial of boundary, ribbon, or of brunnian links.