The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots. Issue 1 (1st March 2018)

• Record Type: Journal Article
• Authors: Tran, Anh T.; Yamaguchi, Yoshikazu
• Is Part Of: Canadian mathematical bulletin =. Volume 61:Issue 1(2018)
• Page Start: 211
• Page End: 224
• Publication Date: 2018-03-01
• Subjects: 57M27 -- 57M50; Reidemeister torsion -- graph manifold -- asymptotic behavior -- exceptional surgery; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2017-021-5
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible $\text{S}{{\text{L}}_{2}}(\mathbb{C})$ -representations of the graph manifold are induced by irreducible metabelian representations of the twist knot group. We also give the set of the limits of the leading coeõcients in the higher dimensional Reidemeister torsion explicitly.