Texas A&M University, Department of
Mathematics, 216 Milner Hall, 22nd of September 2004, 3:00-3:50
Groups and Dynamics Seminar
Dynamical zeta
functions and Nielsen-Reidemeister theory
Alexander Fel'shtyn of Universität
Siegen
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, geometric group theory and
non-commutative geometry. In the talk I will discuss the Reidemeister
and Nielsen zeta functions. These zeta functions count periodic points
of a dynamical system in the presence of a fundamental group. Twisted
Burnside theorem and arithmetical congruences for Reidemeister numbers
will be described. I will explain how dynamical zeta functions give
rise to the Reidemeister torsion, an important topological invariant,
which has useful applications in topology, quantum field theory and
dynamical systems.