In this paper, we determine the total Stiefel-Whitney classes of vector bundles over the product of the complex projective space CP (j) with the quaternionic projective space HP (k). Moreover, we show that every involution fixing CP (2m+1)×HP (k) bounds. AMS subject classifications: 57R85, 57S17, 55N22

1. Two vector bundles E and F over the finite connected CW complex X are /-equivalent, if their sphere-bundles S(E) and S(F) are of the same fiber-homotopy type. If they become /-equivalent after a suitable number of trivial bundles is added to both of them they are stably /-equivalent. This note concerns itself with a new stable /-invariant 6(E), which was suggested by the recent work of Atiya...

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology....

Suppose that (Φ,Mn) is a smooth (Z2)-action on a closed smooth n-dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set F vanish in positive dimension. This paper shows that if dimMn > 2k dimF and each pdimensional part F p possesses the linear independence property, then (Φ,Mn) bounds equivariantly, and in particular,...

Given a manifold M , Milnor and Stasheff studied in [1] the diagonal cohomology class u′′ ∈ Hm(M ×M ;Z/2) that describes the orientation of the tangent bundle, and is related to its Stiefel-Whitney Classes. We generalize this concept to fiber bundles M → E → N where the fiber and base are manifolds, relate it to the diagonal homology class, study the naturality of the construction, give further...

Svctan, D., New plethysm operation, Checn characters of exterior and symmetric powers with applications to Stiefel-Whitney classes of gcassmannians, Theoretical Computer Science 117 (1993) 289-301. In this paper a new plethysm operation is proposed and a technique for coefficient extraction for a fairly general class of symmetric power series (e.g. multiplicative sequences of the theory of ?cha...