Non-commutative Reidemeister torsion and Morse-Novikov theory

Details Non-commutative Reidemeister torsion and Morse-Novikov theory Non-commutative Reidemeister torsion and Morse-Novikov theory

2009-06-23

arxiv.org/abs/0906.4174v5

Proc. Amer. Math. Soc. 138 (2010) 3345-3360

Mathematics

Geometric Topology

12 pages; 13 pages, added important references for the introduction; changed the fixed generator $t$ into the inverse one; 15

Scientific paper

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.

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