Non-commutative Reidemeister Torsion and Morse-novikov Theory
نویسنده
چکیده
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 non-commutative generalization of the result of Hutchings-Lee on the abelian setting. As a consequence we obtain Morse theoretical description of the higher-order Reidemeister torsion.
منابع مشابه
Reidemeister torsion in generalized Morse theory
In two previous papers with Yi-Jen Lee, we defined and computed a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. The present paper gives an a priori proof that this Morse theory invariant is a topological invariant. It is hoped that this will provide a model for possible generalizations to Floer theory. In two papers with Yi-Jen Lee [HL1,...
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