TY - JOUR
T1 - Some results about the Kauffman bracket skein module of the twist knot exterior
AU - Gelca, Rǎzvan
AU - Nagasato, Fumikazu
N1 - Funding Information:
The second author would like to thank Professor Makoto Sakuma for the helpful comments and Professor Mitsuyoshi Kato for his encouragement. The second author was supported by JSPS Research Fellowships for Young Scientists.
PY - 2006/10
Y1 - 2006/10
N2 - 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.
AB - 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.
KW - A-polynomial
KW - Character varieties
KW - Colored Kauffman brackets
KW - Kauffman bracket skein module
KW - Tunnel number
UR - http://www.scopus.com/inward/record.url?scp=33751102911&partnerID=8YFLogxK
U2 - 10.1142/S0218216506004968
DO - 10.1142/S0218216506004968
M3 - Article
AN - SCOPUS:33751102911
SN - 0218-2165
VL - 15
SP - 1095
EP - 1106
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 8
ER -