Table of contents

In this paper, to each many-valued formal group in cobordism theory there are associated generalized cohomology theories, analogous to K-theory and cobordism theory, and a geometric realization of many-valued formal groups in cobordism is obtained. In addition, there is proposed a construction, with the help of which all formal groups known in topology are obtained.

Bibliography: 14 titles.

In this article it is proved that any holomorphic mapping of a compact, nonspherical, strictly pseudoconvex real-analytic hypersurface in an n-dimensional complex manifold (n≥2) onto another such surface extends holomorphically to a neighborhood of the first surface which is independent of the choice of mapping, and that the family of extensions of mappings is equicontinuous in this neighborhood.

Bibliography: 4 titles.

This paper considers generalizations of the Bourgin-Yang theorem. It is shown that if is a continuous mapping of a paracompact free -space into an -dimensional manifold , then, under the condition that (where is the index in the sense of Yang) and for , where the are the Wu classes of , the following inequality holds:

Besides this result, certain " nonsymmetric" versions of the Borsuk-Ulam theorem are proved.

Bibliography: 16 titles.

In this paper it is proved that each infinite-zone potential of the class considered in the paper "Almost periodicity of infinite-zone potentials" (Math. USSR Izv. (1982), No. 2, 249-273) is the uniform limit of finite-zone potentials on the entire real line. The proof is based on a detailed study of the problem of Jacobi inversion on a two-sheeted Riemann surface with an infinite number of branch points.

Bibliography: 5 titles.

The left divisibility problem for semigroups without left cycles is reduced to the same problem for semigroups which describe certain transformations of words in the original semigroup. Using this reduction one can solve positively the word and left divisibility problems for semigroups of the form , where is an arbitrary word in the alphabet .

Bibliography: 5 titles.

Using geometric properties of the orbit space, the author gives a characterization of finite linear groups generated by reflections. Sufficient conditions that the module of covariants for a connected reductive group be free are indicated.

Bibliography: 7 titles.

It is proved that if a function , , can be approximated locally outside its zero set by holomorphic functions, then it can be approximated also on the whole compact set . This implies that if , , and can be approximated by holomorphic functions on , then so can .

Bibliography: 5 titles.

The authors announce the conjecture that a family of K3 surfaces the Artin height of whose generic fiber is greater than 2 does not degenerate; they prove this conjecture for surfaces of degree 2. As a corollary it is shown that a family of supersingular K3 surfaces does not degenerate; i.e., its variety of moduli is complete.

Bibliography: 18 titles.

Many authors have considered the problem of convergence of a random point field to a Poisson field for various types of particle motion. In this article a general construction is presented which yields many of the previously proven results as special cases, along with a number of new examples of models of motion and initial random point fields such that there is convergence to Poisson fields and mixtures of them.

Bibliography: 13 titles.

The Hodge conjecture on algebraic cycles is proved for all simple abelian varieties of prime dimension over the field of complex numbers.

Bibliography: 10 titles.

This paper investigates the approximation of periodic functions of several variables by trigonometric polynomials whose harmonics lie in hyperbolic crosses. It is shown that in many cases the order of the widths, in the sense of Kolmogorov, can be found for classes of functions with a bounded mixed derivative or difference. The possibilities of linear methods of approximation are investigated.

Bibliography: 16 titles.