An analog of the Iwasawa conjecture for a compact hyperbolic threefold

@inproceedings{Sugiyama2006AnAO,
  title={An analog of the Iwasawa conjecture for a compact hyperbolic threefold},
  author={Ken-ichi Sugiyama},
  year={2006}
}
Abstract For a local system on a compact hyperbolic threefold, under a cohomological assumption, we will show that the order of its twisted Alexander polynomial and of the Ruelle L-function at s = 0 coincide. Moreover we will show that their leading constants are also identical. These results may be considered as a solution of a geomeric analogue of the Iwasawa conjecture in the algebraic number theory. 
View PDF on arXiv
17 Citations
Background Citations
4

17 Citations

Citation Type

Citation Type

An analog of the Iwasawa conjecture for a complete hyperbolic threefold of finite volume
For a unitary local system of rank one on a complete hyperbolic threefold of finite volume which has only one cusp, we will compare the order of the Alexander invariant at t=1 and one of…
On a special value of the Ruelle L-function
For a unitary local system of rank one on a complete hyperbolic threefold of finite volume which has only one cusp, the Ruelle L-function is defined. We will show that if the first cohomology group…
Torsions and the Iwasawa Main Conjecture
In this chapter we take up the Iwasawa main conjecture which asserts that the Iwasawa polynomial coincides essentially with the Kubota–Leopoldt p-adic analytic zeta function. According to the analogy…
The propreties of an L-function from a geometric point of view
We will discuss similarities of L-functions between in the number theory and in the geometry. In particular the Hesse-Weil congruent zeta function of a smooth curve defined over a finite field will…
A SURVEY OF TWISTED ALEXANDER POLYNOMIALS
We give a short introduction to the theory of twisted Alexander polynomials of a 3-manifold associated to a representation of its fundamental group. We summarize their formal properties and we…
A special value of Ruelle L-function and the theorem of Cheeger and Muller
We will show a theorem of a type of Cheeger and Muller for a noncompact complete hyperbolic threefold of finite vulume. As an application we will compute a special value of Ruelle L-function at the…
ANALYTIC TORSION AND RUELLE ZETA FUNCTIONS FOR HYPERBOLIC MANIFOLDS WITH CUSPS
The Taylor expansion of Ruelle L-function at the origin and the Borel regulator
We will prove that Ruelle L-function for a cuspidal local system on an odd dimensional hyperbolic manifold with finite volume satisfies a functional equation and an analog of the Riemann hypothesis.…
The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps
In this paper, we study the Ruelle zeta function and the Selberg zeta functions attached to the fundamental representations for real hyperbolic manifolds with cusps. In particular, we show that they…
Arithmetic Riemann-Roch isomorphism, Chern-Simons invariant and Liouville action
Using the arithmetic Schottky uniformization theory, we show the arithmeticity of PSL_2(C) Chern-Simons invariant, and give an explicit formula of the arithmetic Riemann-Roch isomorphism for…
...
...

References

SHOWING 1-10 OF 10 REFERENCES
Twisted Alexander polynomial and Reidemeister torsion
In 1992, Wada [4] defined the twisted Alexander polynomial for finitely presentable groups. Let Γ be a finitely presentable group. We suppose that the abelianization Γ/[Γ, Γ] is a free abelian group…
TWISTED ALEXANDER INVARIANTS, REIDEMEISTER TORSION, AND CASSON–GORDON INVARIANTS
Analytic torsion and closed geodesics on hyperbolic manifolds
Pour une variete hyperbolique orientee fermee X et ρ une representation orthogonale de Π 1 X, on definit une fonction zeta de type Ruelle Rρ(s) pour Re(s) grand comme le produit sur les geodesiques…
WHITEHEAD TORSION BY
In 1935, Reidemeister, Franz and de Rham introduced the concept of "torsion" for certain finite simplicial complexes. For example let X be a finite complex whose fundamental group TTIX is cyclic of…
Class fields of abelian extensions of Q
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 0. Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…
Infinite cyclic coverings
  • J. G. Hocking, editor, Conference on the Topology of Manifolds, pages 115–133. PWS Publishing Company
  • 1968
J. Milnor. Whitehead torsion. Bull. Amer. Math. Soc
  • J. Milnor. Whitehead torsion. Bull. Amer. Math. Soc
  • 1966
Twisted Alexander invarinants
  • Reidemeister torsion, and Casson-Gordon invariants. Topology, 38(3):635–661
  • 1999
Twisted Alexander invarinants , Reidemeister torsion , and CassonGordon invariants
  • Topology
  • 1999
An analogue of the iwasawa conjecture for a hyperbolic threefold of finite volume
  • An analogue of the iwasawa conjecture for a hyperbolic threefold of finite volume