SOME RESULTS ABOUT THE KAUFFMAN BRACKET SKEIN MODULE OF THE TWIST KNOT EXTERIOR.

In this paper, we list in explicit form the factoring relations of the Kauffman bracket skein module (KBSM for short) of a twist knot exterior. This is done using curves decorated by characters of irreducible SL(2, ℂ)-representations. In the process, we exhibit a relation which holds in the KBSM of the knot exterior, called the minimal relation. In the final section we prove that, when specializing the variable of the Kauffman bracket at t = -1, the minimal relation becomes the defining polynomial of the SL(2, ℂ)-character variety of the twist knot. [ABSTRACT FROM AUTHOR]