On Sectioning multiples of vector bundles and more general homomorphism bundles.
On sectioning tangent bundles and other vector bundles
This paper has two parts. Part one is mainly intended as a general introduction to the problem of sectioning vector bundles (in particular tangent bundles of smooth manifolds) by everywhere linearly independent sections, giving a survey of some ideas, methods and results.Part two then records some recent progress in sectioning tangent bundles of several families of specific manifolds.
On Seiberg-Witten equationsοn symplectic 4-manifolds
We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.
On self-dual pseudo-connections on some orbifolds.
On S-Equivalence of Seifert Matrices.
On Shikata's Distance between differentiable Structures.
On signatures and a subgroup of a central extension to the mapping class group.
On signatures associated with ramified coverings and embedding problems
Given a cohomology class there is a smooth submanifold Poincaré dual to . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in . This note summarizes some results on the question: how does the divisibility of restrict the dual submanifolds in this class ? A formula for signatures associated with a -fold ramified cover of branched along is given and a proof is included in case .
On simple fibered knots in S5 and the existence of decomposable algebraic 3-knots.
On singular cut-and-pastes in the 3-space with applications to link theory.
In the study of surfaces in 3-manifolds, the so-called ?cut-and-paste? of surfaces is frequently used. In this paper, we generalize this method, in a sense, to singular-surfaces, and as an application, we prove that two collections of singular-disks in the 3-space R3 which span the same trivial link are link-homotopic in the upper-half 4-space R3 [0,8) keeping the link fixed. Throughout the paper, we work in the piecewise linear category, consisting of simplicial complexes and piecewise linear maps....
On singularities of Hamiltonian mappings
The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
On slice knots in the complex projective plane.
We investigate the knots in the boundary of the punctured complex projective plane. Our result gives an affirmative answer to a question raised by Suzuki. As an application, we answer to a question by Mathieu.
On small geometric invariants of 3-manifolds.
On smooth structures of potential surfaces of general type homeomorphic to rational surfaces.
On some applications of infinite-dimensional manifolds to the theory of shape
On some components of moduli space of surfaces of general type
On some directions in the development of jet calculus
Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliated manifold morphisms are presented. Although the paper has mainly a survey character, it also includes new results: jets modulo multifoliations are introduced and their relation to (R,S,Q)-jets is demonstrated.
On some operation on sets of mappings
On some rational fibrations with nonvanishing Massey products over homogeneous spaces
The main result of this brief note asserts, incorrectly, that there exists a rational fibration whose total space admits nonzero Massey products. The methods used would be appropriate for showing results of this kind, if the circumstances were to allow for it. Unfortunately the author makes a simple, but nonetheless fatal, computational error in his calculation that ostensibly shows the existence of a nonzero Massey product (p. 249, 1.13: . In fact, for any rational fibration the total space...