Related papers: Counting zeros of closed 1-forms
We introduce a new tool to study the spectral type of rank one transformations using the method of central limit theorem for trigonometric sums. We get some new applications.
A simple method is proposed for deforming $A_\infty$-algebras by means of the resolution technique. The method is then applied to the associative algebras of polynomial functions on quantum superspaces. Specifically, by introducing suitable…
The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…
The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions.…
In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…
We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.
We investigate deformations of free and linear free divisors. We introduce a complex similar to the de Rham complex whose cohomology calculates deformation spaces. This cohomology turns out to be zero for many linear free divisors and to be…
It is shown that the topological phenomenon "zero in the continuous spectrum", discovered by S.P.Novikov and M.A.Shubin, can be explained in terms of a homology theory on the category of finite polyhedra with values in certain abelian…
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…
We consider recently developed Cohomological Field Theory soliton counting diagram technique for Khovanov and Khovanov-Rozansky invariants [1,2]. Although the expectation to obtain a new way for computing the invariants has not yet come…
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also…
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply…
Let $M$ be a closed oriented manifold of dimension $n$ and $\omega$ a closed 1-form on it. We discuss the question whether there exists a Riemannian metric for which $\omega$ is co-closed. For closed 1-forms with nondegenerate zeros the…
In this paper we develope a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known Morsification results for non-isolated singulatities and…
If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form which linearly deforms into contact forms, then M supports a K-contact form. On the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if and…
Let $C$ be a complex affine reduced curve, and denote by $H^1(C)$ its first truncated cohomology group, i.e. the quotient of all regular differential 1-forms by exact 1-forms. First we introduce a nonnegative invariant $\mu'(C,x)$ that…
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. As a consequence we obtain new topological lower bounds on…
Versal deformation of a matrix A is a normal form to which all matrices A + E, close to A, can be reduced by similarity transformation smoothly depending on the entries of A + E. In this paper we discuss versal deformations and their use in…