Morse-Novikov critical point theory, Cohn localization and Dirichlet units

In this paper we construct a Universal chain complex, counting zeros of closed 1-forms on a manifold. The Universal complex is a refinement of the well known Novikov complex; it relates the homotopy type of the manifold, after a suitable noncommutative localization, with the numbers of zeros of different indices which may have closed 1-forms within a given cohomology class. The Main Theorem of the paper generalizes the result of a joint paper with A. Ranicki, which treats the special case of closed 1-forms having integral cohomology classes. The present paper also describes a number of new inequalities, giving topological lower bounds on the number of zeroes of closed 1-forms. In particular, such estimates are provided by the homology of flat line bundles with monodromy described by complex numbers which are not Dirichlet units

Early exposure to both sign and spoken language for children who are deaf or hard of hearing: Might it help spoken language development?

The literature on the benefits and deficits of bilingualism is reviewed with an emphasis on sign/spoken bilingualism and on the population of deaf or hard of hearing children. Since there are a limited number of reports on sign/spoken bilingualism for these children, a research plan is outlined for a large study whose results could have a significant impact on oral education policy and spoken language development in deaf or hard of hearing children

Zeros of closed 1-forms, homoclinic orbits, and Lusternik - Schnirelman theory

In this paper we study topological lower bounds on the number of zeros of closed 1-forms without Morse type assumptions. We prove that one may always find a representing closed 1-form having at most one zero. We introduce and study a generalization $cat(X,\xi)$ of the notion of Lusternik - Schnirelman category, depending on a topological space $X$ and a cohomology class $\xi\in H^1(X;\R)$. We prove that any closed 1-form has at least $cat(X,\xi)$ zeros assuming that it admits a gradient-like vector field with no homoclinic cycles. We show that the number $cat(X,\xi)$ can be estimated from below in terms of the cup-products and higher Massey products. This paper corrects some statements made in my previous papers on this subject.Comment: 34 pages. A refernce adde