we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

Characteristic classes play an essential role in the study of global properties of vector bundles. Particularly important is the Euler class of real orientable vector bundles. A de Rham representative of the Euler class (for tangent bundles) first appeared in Chern’s generalisation of the Gauss-Bonnet theorem to higher dimensions. The representative is the Pfaffian of the curvature, whose cohom...

We investigate the following problems. Given a spherical fibration, does the Whitehead square of its homotopy Thom class vanish? If so, is the homotopy Thorn class a cyclic homotopy class?

In this paper we identify conditions under which the cohomology H∗(ΩMξ; k) for the loop space ΩMξ of the Thom space Mξ of a spherical fibration ξ ↓ B can be a polynomial ring. We use the Eilenberg–Moore spectral sequence which has a particularly simple form when the Euler class e(ξ) ∈ H(B; k) vanishes, or equivalently when an orientation class for the Thom space has trivial square. As a consequ...

The global behavior of singularities is governed by their Thom polynomials (cf. [35], [14], [1], [11], [31]). Knowing the Thom polynomial of a singularity η, denoted T η, one can compute the cohomology class represented by the η-points of a map. We do not attempt here to survey all activities related to computations of Thom polynomials, which are difficult tasks in general. In the present paper...

commutes up to homotopy where T is the map that exchanges factors. Let L be a space and let be a fibration over L classified by a mapf L BF (the classifying space of stable spherical fibrations). We can form the Thom spectrum T(f) of f as a suspension spectrum by letting (T(f)) be the Thorn complex of L n--YBFn where L is the n-skeleton of L. This makes T(f)-{(T(f))n) into a suspension spectrum...