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Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
 
Alexander Fel’shtyn University of Greifswald, Greifswald, Germany
Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
eBook ISBN:  978-1-4704-0290-7
Product Code:  MEMO/147/699.E
List Price: $57.00
MAA Member Price: $51.30
AMS Member Price: $34.20
Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
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Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion
Alexander Fel’shtyn University of Greifswald, Greifswald, Germany
eBook ISBN:  978-1-4704-0290-7
Product Code:  MEMO/147/699.E
List Price: $57.00
MAA Member Price: $51.30
AMS Member Price: $34.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1472000; 146 pp
    MSC: Primary 58; Secondary 55; 57;

    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.

    Readership

    Graduate students and research mathematicians interested in global analysis, analysis on manifolds.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1472000; 146 pp
MSC: Primary 58; Secondary 55; 57;

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.

Readership

Graduate students and research mathematicians interested in global analysis, analysis on manifolds.

  • Chapters
  • Introduction
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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