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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Non-commutative Reidemeister torsion and Morse-Novikov theory


Author: Takahiro Kitayama
Journal: Proc. Amer. Math. Soc. 138 (2010), 3345-3360
MSC (2010): Primary 57Q10; Secondary 57R70
Published electronically: April 30, 2010
MathSciNet review: 2653964
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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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Additional Information

Takahiro Kitayama
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: kitayama@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10418-3
PII: S 0002-9939(10)10418-3
Keywords: Reidemeister torsion, Morse-Novikov complex, derived series
Received by editor(s): September 2, 2009
Received by editor(s) in revised form: December 28, 2009
Published electronically: April 30, 2010
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.