Franklin

Dynamical zeta functions, Nielsen theory, and Reidemeister torsion / Alexander Felʹshtyn.

Author/Creator:
Felʹshtyn, Alexander, 1952- author.
Publication:
Providence, Rhode Island : American Mathematical Society, 2000.
Format/Description:
Book
1 online resource (165 p.)
Series:
Memoirs of the American Mathematical Society ; no. 699.
Memoirs of the American Mathematical Society, 0065-9266 ; number 699
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Subjects:
Functions, Zeta.
Fixed point theory.
Piecewise linear topology.
Form/Genre:
Electronic books.
Language:
English
Contents:
""Contents""; ""Introduction""; ""0.1 From Riemann zeta function to dynamical zeta functions""; ""0.1.1 Riemann zeta function""; ""0.1.2 Problems concerning zeta functions""; ""0.1.3 Important types of zeta functions""; ""0.1.4 Hasse-Weil zeta function""; ""0.1.5 Dynamical zeta functions""; ""0.2 Dynamical zeta functions and Nielsen fixed point theory""; ""0.3 Congruences for Reidemeister numbers""; ""0.4 Reidemeister torsion""; ""0.5 Table of contents""; ""1 Nielsen Fixed Point Theory""; ""1.1 History""; ""1.2 Lifting classes and fixed point classes""; ""1.2.1 The influence of a homotopy""
""1.3 Reidemeister numbers""""1.3.1 Reidemeister numbers of a continuous map""; ""1.3.2 Reidemeister numbers of a group endomorphism""; ""1.4 Nielsen numbers of a continuous map""; ""1.4.1 The fixed point index""; ""1.4.2 Nielsen numbers""; ""1.4.3 The least number of fixed points""; ""2 The Reidemeister zeta function""; ""2.1 A Convolution Product""; ""2.2 Pontryagin Duality""; ""2.3 Eventually commutative endomorphisms""; ""2.3.1 Trace formula for the Reidemeister numbers of eventually commutative endomorphisms""
""2.3.2 Rationality of Reidemeister zeta functions of eventually commutative endomorphisms - first proof""""2.3.3 Functional equation for the Reidemeister zeta function of an eventually commutative endomorphism""; ""2.3.4 Rationality of Reidemeister zeta functions of eventually commutative endomorphisms - second proof""; ""2.3.5 Connection of the Reidemeister zeta function with the Lefschetz zeta function of the dual map""; ""2.4 Endomorphisms of finite groups""; ""2.5 Endomorphisms of the direct sum of a free Abelian and a finite group""; ""2.6 Endomorphisms of nilpotent groups""
""2.6.1 Functional equation""""2.7 The Reidemeister zeta function and group extensions""; ""2.8 The Reidemeister zeta function of a continuous map""; ""2.8.1 The Reidemeister zeta function of a continuous map and Serre bundles""; ""3 The Nielsen zeta function""; ""3.1 Radius of Convergence of the Nielsen zeta function""; ""3.1.1 Topological entropy""; ""3.1.2 Algebraic lower estimation for the Radius of Convergence""; ""3.2 Nielsen zeta function of a periodic map""; ""3.3 Orientation-preserving homeomorphisms of a compact surface""
""3.3.1 Geometry of the Mapping Torus and Radius of Convergence""""3.4 The Jiang subgroup and the Nielsen zeta function""; ""3.5 Polyhedra with finite fundamental group""; ""3.6 Nielsen zeta function in other special cases""; ""3.6.1 Pseudo-Anosov homeomorphism of a compact surface""; ""3.7 The Nielsen zeta function and Serre bundles""; ""3.8 Examples""; ""4 Reidemeister and Nielsen zeta functions modulo normal subgroup, minimal dynamical zeta functions""; ""4.1 Reidemeister and Nielsen zeta functions modulo a normal subgroup""
""4.1.1 Radius of Convergence of the mod K Nielsen zeta function""
Notes:
"Volume 147, number 699 (third of 4 numbers)."
Includes bibliographical references.
Description based on print version record.
ISBN:
1-4704-0290-4