Reidemeister torsion in generalized Morse theory
نویسندگان
چکیده
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,...
متن کاملCircle-Valued Morse Theory and Reidemeister Torsion
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...
متن کاملNon-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...
متن کاملA Generalized Morse Theory
1. Abstract theory. Let M be a C-Riemannian manifold without boundary modeled on a separable Hubert space (see Lang [3]). For pÇzM we denote by ( , )p the inner product in the tangent space Mp and we define a function || || on the tangent bundle T(M) by ||z>|| = (v, v)J for vÇzMp. Given p and q in the same component of M we define p(p, q)==lnïfl\\<r'(t)\\dtt where the Inf is over all C 1 paths ...
متن کاملHigher Franz - Reidemeister Torsion
In this expository article I will discuss the theory of higher Franz-Reidemeister torsion and its application to the construction of non-trivial classes in the algebraic K-theory of elds. I will also explain how these ideas may be used to construct classes in the cohomology of the Torelli group.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2002
ISSN: 0933-7741,1435-5337
DOI: 10.1515/form.2002.010