Dynamical zeta functions, Nielsen theory and Reidemeister torsion
About this Title
Publication: Memoirs of the American Mathematical Society
Publication Year 2000: Volume 147, Number 699
ISBNs: 978-0-8218-2090-2 (print); 978-1-4704-0290-7 (online)
MathSciNet review: 1697460
MSC (1991): Primary 37C30; Secondary 37C15, 37C25, 55M20
In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Graduate students and research mathematicians interested in global analysis, analysis on manifolds.
Table of Contents
- 1. Nielsen fixed point theory
- 2. The Reidemeister zeta function
- 3. The Nielsen zeta function
- 4. Reidemeister and Nielsen zeta functions modulo normal subgroup, minimal dynamical zeta functions
- 5. Congruences for Reidemeister and Nielsen numbers
- 6. The Reidemeister torsion