2005/12/31 by Yoshikazu Yamaguchi · 12 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Abelian group #Alexander polynomial #Anatomy #Bifurcation #Combinatorics #Connective tissue disorders research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot invariant #Knot theory #Mathematics #Nonlinear system #Physics #Pure mathematics #Torsion (gastropod) #Trefoil knot #math.GT #msc:57M05 #msc:57M25 #msc:57M27 #msc:57Q10
paper · pdf · doi:10.2140/agt.2007.7.1485
published in Algebraic & Geometric Topology 7(3), 1485-1507 (Mathematical Sciences Publishers) · to appear in Algebraic and Geometric Topology
arxiv created 2007/10/31 · openalex publication_date 2007/11/14 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the Reidemeister torsion associated with SL 2 .-/representations of a knot group. A bifurcation point in the SL 2 .-/character variety of a knot group is a character which is given by both an abelian SL 2 .-/representation and a nonabelian one. We show that there exist limits of the non-acyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot in this paper.