Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 57Q10, 57R70

Retrieve articles in all journals with MSC (2010): 57Q10, 57R70

Additional Information

Takahiro Kitayama
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

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.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia