On compact subsets of an n-manifold
On complete intersections
We construct closed complex submanifolds of which are differential but not holomorphic complete intersections. We also prove a homotopy principle concerning the removal of intersections with certain complex subvarieties of .
On complex structures in 8-dimensional vector bundles.
On complex vector bundles on projective threefolds.
On condition of a stratified mapping
For a stratified mapping , we consider the condition concerning the kernel of the differential of . We show that the condition is equivalent to the condition which has a more obvious geometric content.
On conformally flat Lorentz parabolic manifolds
We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.
On construction of signature of quadratic forms on infinite-dimensional abstract spaces.
On constructions of generalized skein modules
Józef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors is given, and the corresponding background is developed. The possible coloring of fields by elements of...
On contractible open 3-manifolds.
On convex metric spaces II
On cotangent bundles of some natural bundles
The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle ; 2. Natural operators transforming vector fields on manifolds into functions on the cotangent bundle of . It is deduced that under certain assumptions on , all natural operators of the second type can be constructed through those of the first one.
On Countable Dense and Strong Local Homogeneity
We present an example of a connected, Polish, countable dense homogeneous space X that is not strongly locally homogeneous. In fact, a nontrivial homeomorphism of X is the identity on no nonempty open subset of X.
On countable dense and strong n-homogeneity
We prove that if a space X is countable dense homogeneous and no set of size n-1 separates it, then X is strongly n-homogeneous. Our main result is the construction of an example of a Polish space X that is strongly n-homogeneous for every n, but not countable dense homogeneous.
On Critical Sets of Distance Functions to a taut Submanifold.
On Culler-Shalen seminorms and Dehn filling.
On curvature constructions of symplectic forms
We generalize the result of Lerman [Letters Math. Phys. 15 (1988)] concerning the condition of fatness of the canonical connection in a certain principal fibre bundle. We also describe new classes of symplectically fat bundles: twistor budles over spheres, bundles over quaternionic Kähler homogeneous spaces and locally homogeneous complex manifolds.
On Cyclic Branched Coverings of Spheres.
On decomposition of 3-polyhedra into a Cartesian product
On decomposition of polyhedra into a Cartesian product of 1-dimensional and 2-dimensional factors
On deformations of holomorphic foliations
Given a non-singular holomorphic foliation on a compact manifold we analyze the relationship between the versal spaces and of deformations of as a holomorphic foliation and as a transversely holomorphic foliation respectively. With this purpose, we prove the existence of a versal unfolding of parametrized by an analytic space isomorphic to where is smooth and : is the forgetful map. The map is shown to be an epimorphism in two situations: (i) if , where is the sheaf of...