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Non-commutative Reidemeister torsion and Morse-Novikov theory
Author(s):
Takahiro
Kitayama
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3345-3360.
MSC (2010):
Primary 57Q10;
Secondary 57R70
Posted:
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:
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
Posted:
April 30, 2010
Communicated by:
Daniel Ruberman
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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