TY - JOUR
T1 - Non-abelian reidemeister torsion for twist knots
AU - Dubois, Jérôme
AU - Huynh, Vu
AU - Yamaguchi, Yoshikazu
N1 - Funding Information:
The first author is supported by the European Community with Marie Curie Intra-European Fellowship (MEIF-CT-2006-025316). While writing the paper, J.D. visited the CRM. He thanks the CRM for hospitality. J.D. is partially supported by ANR “Géométrie et Analyse des Conjectures du Volume”. The second author wishes to thank the Institute of Mathematical Sciences, National University of Singapore for hospitality and support. The third author is partially supported by the 21st century COE program at Graduate School of Mathematical Sciences, University of Tokyo. On finishing the paper, J.D. visited the Department of Mathematics of Tokyo Institute of Technology. J.D. and Y.Y. wish to thank Hitoshi Murakami and TiTech’s Department of Mathematics for invitation and hospitality. The authors also want to thank Joan Porti for his comments and remarks.
PY - 2009/3
Y1 - 2009/3
N2 - This paper gives an explicit formula for the SL2(complexes;)- non-abelian Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the non-abelian Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot.
AB - This paper gives an explicit formula for the SL2(complexes;)- non-abelian Reidemeister torsion as defined in [6] in the case of twist knots. For hyperbolic twist knots, we also prove that the non-abelian Reidemeister torsion at the holonomy representation can be expressed as a rational function evaluated at the cusp shape of the knot.
KW - Adjoint representation
KW - Character variety
KW - Cusp shape
KW - Reidemeister torsion
KW - Twist knot
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U2 - 10.1142/S0218216509006951
DO - 10.1142/S0218216509006951
M3 - Article
AN - SCOPUS:65249121370
SN - 0218-2165
VL - 18
SP - 303
EP - 341
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 3
ER -