Ajay Singh Thakur

Note on the characteristic rank of vector bundles

We define the notion of characteristic rank, charrankX(ξ), of a real vector bundle ξ over a connected finite CW-complex X. This is a bundle-dependent version of the notion of characteristic rank introduced by Július Korbaš in 2010. We obtain bounds for the cup length of manifolds in terms of the characteristic rank of vector bundles generalizing a theorem of Korbaš and compute the characteristic rank of vector bundles over the Dold manifolds, the Moore spaces and the stunted projective spaces amongst others.

On trivialities of Stiefel-Whitney classes of vector bundles over iterated suspensions of Dold manifolds

A space X is called W-trivial if for every vector bundleover X, the total Stiefel-Whitney class W(�) = 1. In this article we shall investigate whether the suspensions of Dold manifolds, � k D(m,n), is W-trivial or not.

Characteristic rank of vector bundles over Stiefel manifolds

The characteristic rank of a vector bundle ξ over a finite connected CW-complex X is by definition the largest integer

Nonexistence of almost complex structures on the product S2m×M

{k, 0 \leq k \leq \mathrm{dim}(X)}

Vector bundles over iterated suspensions of stunted real projective spaces

, such that every cohomology class

Infinitesimal Deformations and Brauer Group of Some Generalized Calabi--Eckmann Manifolds

{x \in H^{j}(X;\mathbb{Z}_2), 0 \leq j \leq k}