15 citations · 43 across the 6 of their papers we have counts for
8 papers · 1 filter
The Morse-Novikov theory of circle-valued functions and noncommutative localization
Michael Farber, Andrew Ranicki
We use noncommutative localization to construct a chain complex which counts the critical points of a circle-valued Morse function on a manifold, generalizing the Novikov complex.…
Topology of closed 1-forms and their critical points
Michael Farber
In this paper I suggest an alternative approach (using generic flat bundles and higher Massey products) to a Lusternik-Schnirelman type theory for closed 1-forms (cf. also math.DG/…
Lusternik-Schnirelman theory for closed 1-forms
Michael Farber
S.P.Novikov developed an analog of the Morse theory for closed 1-forms. In this paper I suggest an analog of the Lusternik - Schnirelman theory for closed 1-forms.
Von Neumann Betti numbers and Novikov type inequalities
Michael Farber
It is shown that the Novikov inequalities for critical points of closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a corollary we obtain a va…
Massey products and critical points
Michael Farber
In this note I use cup-products and higher Massey products to find topological lower bounds on the number of geometrically distinct critical points of any closed 1-form in a given…
Absolute torsion
Michael Farber, Vladimir Turaev
In this paper we use the results of our previous work in order to compute the phase of the torsion of an Euler structure in terms of its characteristic class. Also, we introduce he…