Texas A&M University, Department of
Mathematics, 216 Milner Hall, 17th of November 2004, 3:00-3:50
Groups and Dynamics Seminar
Reidemeister
torsion and dynamical zeta
functions
Alexander Fel'shtyn of Universität
Siegen
Reidemeister torsion is a very important topological invariant which
has useful applications in the theory of manifolds and
knots, theory of elliptic operators and quantum field theory. Recently,
the Reidemeister torsion has found interesting applications in
dynamical systems theory. A connection between the Weil type
dynamical zeta functions and the Reidemeister torsion was established
by Milnor and Fried . In the talk we discuss a connection between the
Reidemeister torsion and Reidemeister zeta function of a group
automorphism. The result is obtained by expressing the Reidemeister
zeta function in terms of the Weil zeta function of the unitary dual
map, and then applying the theorem of Milnor and Fried. What this means
is that the Reidemeister torsion counts the twisted conjugacy classes
of all iterates of a group automorphism and fixed point classes of all
iterates of a map, i.e. periodic point classes of a map.