%0 Journal Article
%T Non-commutative Reidemeister torsion and Morse-Novikov theory
%A Takahiro Kitayama
%J Mathematics
%D 2009
%I arXiv
%X Given a circle-valued Morse function of a closed oriented manifold, we prove that Reidemeister torsion over a non-commutative formal Laurent polynomial ring equals the product of a certain non-commutative Lefschetz-type zeta function and the algebraic torsion of the Novikov complex over the ring. This paper gives a generalization of the result of Hutchings and Lee on abelian coefficients to the case of skew fields. As a consequence we obtain a Morse theoretical and dynamical description of the higher-order Reidemeister torsion.
%U http://arxiv.org/abs/0906.4174v5