Higher Franz-Reidemeister Torsion

2002 ◽  
Author(s):  
Kiyoshi Igusa
Keyword(s):  
Reidemeister Torsion

scholarly journals The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots

2018 ◽  
Vol 61 (1) ◽  
pp. 211-224 ◽  
Author(s):  
Anh T. Tran ◽  
Yoshikazu Yamaguchi
Keyword(s):  
Asymptotic Behavior ◽  
Reidemeister Torsion ◽  
Graph Manifold ◽  
Higher Dimensional ◽  
Graph Manifolds

AbstractWe 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 SL2()-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.

scholarly journals Mutation and SL(2,ℂ)–Reidemeister torsion for hyperbolic knots

2012 ◽  
Vol 12 (4) ◽  
pp. 2049-2067
Author(s):  
Pere Menal-Ferrer ◽  
Joan Porti
Keyword(s):  
Reidemeister Torsion

scholarly journals A VOLUME FORM ON THE KHOVANOV INVARIANT

2012 ◽  
Vol 21 (04) ◽  
pp. 1250032
Author(s):  
JUAN ORTIZ-NAVARRO
Keyword(s):  
Chain Complex ◽  
Khovanov Homology ◽  
Volume Form ◽  
Reidemeister Torsion ◽  
Homology Groups ◽  
Numerical Invariant ◽  
Reidemeister Moves ◽  
Invariant Volume ◽  
Knots And Links

The Reidemeister torsion construction can be applied to the chain complex used to compute the Khovanov homology of a knot or a link. This defines a volume form on Khovanov homology. The volume form transforms correctly under Reidemeister moves to give an invariant volume on the Khovanov homology. In this paper, its construction and invariance under these moves is demonstrated. Also, some examples of the invariant are presented for particular choices for the bases of homology groups to obtain a numerical invariant of knots and links. In these examples, the algebraic torsion seen in the Khovanov chain complex when homology is computed over ℤ is recovered.

Sign in / Sign up

Export Citation Format

Share Document