Non-commutative Reidemeister torsion and Morse-Novikov theory
نویسندگان
چکیده
منابع مشابه
Non-commutative Reidemeister Torsion and Morse-novikov Theory
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 set...
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We compute an invariant counting gradient flow lines (including closed orbits) in S-valued Morse theory, and relate it to Reidemeister torsion for manifolds with χ = 0, b1 > 0. Here we extend the results in [6] following a different approach. However, this paper is written in a self-contained manner and may be read independently of [6]. The motivation of this work is twofold: on the one hand, i...
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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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This is the first part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, IF . The Floer homology can be trivial in many variants of the Floer theory; it is therefore interesting to consider more refined invariants of the Floer complex. We consider one such instance—the Reidemeister torsion τF of the FloerNovikov complex of (possibly non-hamiltonian) symplec...
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Given a 3–manifold the second author defined functions δn : H (M ;Z) → N, generalizing McMullen’s Alexander norm, which give lower bounds on the Thurston norm. We reformulate these invariants in terms of Reidemeister torsion over a non– commutative multivariable Laurent polynomial ring. This allows us to show that these functions are semi-norms.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-10-10418-3