Non-commutative Reidemeister torsion and Morse-Novikov theory

Kitayama, Takahiro

doi:10.1090/S0002-9939-10-10418-3

Non-commutative Reidemeister torsion and Morse-Novikov theory
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by Takahiro Kitayama

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

DOI: https://doi.org/10.1090/S0002-9939-10-10418-3

Published electronically: April 30, 2010

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Abstract:

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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