Non-commutative Reidemeister torsion and Morse-Novikov theory

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Kitayama, Takahiro
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Abstract
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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.
Comment: 12 pages; 13 pages, added important references for the introduction; changed the fixed generator $t$ into the inverse one; 15 pages, redefined the non-commutative zeta function; to appear in Proceedings of the American Mathematical Society
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Mathematics - Geometric Topology, 57Q10, 57R70
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