On some spaces which are covered by a product space
In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the...
On Some Spaces which can be Partioned by the Rational Line.
On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.
Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.
On Stable Parallelizability of Gk,n and Related Manifolds.
On sums of algebraic surfaces.
On symmetric group actions on spin 4-manifolds.
On symplectic cobordism of real projective plane.
This note answers a question of V. V. Vershinin concerning the properties of Buchstaber's elements Θ2i+1(2) in the symplectic cobordism ring of the real projective plane. It is motivated by Roush's famous result that the restriction of these elements to the projective line is trivial, and by the relationship with obstructions to multiplication in symplectic cobordism with singularities.
On the algebraic structure on the jet prolongations of fibred manifolds
On the Buchstaber subring in .
On the Cech bicomplex associated with foliated structures
For a codimension foliation on a manifold, defines the Godbillon-Vey class. We show that itself defines a certain cohomology class, via the Cech bicomplex.
On the Chern character of glued bundles
On the classification of G-spheres II: PL automorphism groups.
On the classification of tight contact structures. I.
On the Classification of Topological 4-Manifolds with Finite Fundamental Group.
On the Cohomology of Bigraded Forms Associated With Foliated Structures
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces
The continuous cohomology theory of the Lie algebra of complex analytic vector fields on an open Riemann surface is studied. We show that the cohomology group with coefficients in the -module of germs of complex analytic tensor fields on the product space decomposes into the global part derived from the homology of and the local part coming from the coefficients.
On the Construction of Codimension Two Minimal Immersions of Exotic Spheres into Euclidean Spheres. II.
On the construction of constant mean curvature imbeddings of exotic and/or knotted spheres into Sn (1).