Representing homology classes by locally flat 2-spheres

We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.Partially supported by the NSF.     

Strictly nilpotent elements and bispectral operators in the Weyl algebra

In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc).     

Degenerations of binary Lie and nilpotent Malcev algebras

We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ?. In particular, we describe all irreducible components of these varieties.     

Subgroup separability of certain generalized free products of nilpotent-by-finite groups

In this paper, we show that certain generalized free products of nilpotent-by-finite groups are subgroup separable when the amalgamated subgroup is h× D where D is in the center of both factors.     

c-capability of Lie algebras with the derived subalgebra of dimension two

The current article is devoted to classify the c-capability of finite dimensional nilpotent Lie algebras with the derived subalgebra of dimension two.     

Generalizations of P. Lévy's inversion theorem

We extend the Lévy inversion formula for the recovery of a bounded measure over $\text{R}$ from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group. All our results are direct generalizations of known inversions for $\text{R}$.     

Pointwise bounds for L 2 eigenfunctions on locally symmetric spaces

We prove pointwise bounds for L ² eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with -rank one if the corresponding eigenvalues lie below the continuous part of the L ² spectrum. Furthermore, we use these bounds in order to obtain some results concerning the L ^p spectrum.     

Morse–Novikov cohomology of locally conformally Kähler manifolds

A locally conformally Kähler (LCK) manifold is a complex manifold admitting a Kähler covering, with the monodromy acting on this covering by holomorphic homotheties. We define three cohomology invariants, the Lee class, the Morse–Novikov class, and the Bott–Chern class, of an LCK-structure. These invariants play together the same role as the Kähler class in Kähler geometry. If these classes coincide for two LCK-structures, the difference between these structures can be expressed by a smooth potential, similar to the Kähler case. We show that the Morse–Novikov class and the Bott–Chern class of a Vaisman manifold vanish. Moreover, for any LCK-structure on a manifold, admitting a Vaisman structure, we prove that its Morse–Novikov class vanishes. We show that a compact LCK-manifold M$M$ with vanishing Bott–Chern class admits a holomorphic embedding into a Hopf manifold, if _dimCM?3${dim}_{\mathbb{C}}M?3$, a result which parallels the Kodaira embedding theorem.