Obstructions for Clifford Structures on Vector Bundles.
On Framed Cobordism Classes Representable on a Fixed Manifold.
On Killing Characteristic Classes by Cobordism.
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 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 symmetric group actions on spin 4-manifolds.
On the algebraic structure on the jet prolongations of fibred manifolds
On the Geometric Weight System of Topological Actions on Cohomology Quaternionic Projective Spaces.
On the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds.
On the number of non-equivalent differentiable structures on 4-Manifolds.
On the topology of positively curved Bazaikin spaces
We explore some aspects of the topology of the family of 13-dimensional Bazaikin spaces. Using the computation of their homology rings, Pontryagin classes and linking forms, we show that there is only one Bazaikin space that is homotopy equivalent to a homogeneous space, i.e., the Berger space. Moreover, it is easily shown that there are only finitely many Bazaikin spaces in each homeomorphism type and that there are only finitely many positively curved ones for a given cohomology ring. In fact,...
Orthogonal polynomials represented by CW-spheres.