BP-cohomology of projective Stiefel manifolds

TL;DR

This paper computes the BP-cohomology of complex projective Stiefel manifolds using spectral sequences and applies these results to study equivariant maps, advancing understanding in algebraic topology.

Contribution

It introduces a method to compute BP-cohomology of Stiefel manifolds and applies BP-operations to derive new results on equivariant maps.

Findings

BP-cohomology of complex projective Stiefel manifolds computed

Spectral sequence method developed for these calculations

New results on equivariant maps between Stiefel manifolds obtained

Abstract

In this paper, we compute the BP-cohomology of complex projective Stiefel manifolds. The method involves the homotopy fixed point spectral sequence, and works for complex oriented cohomology theories. We also use these calculations and BP-operations to prove new results about equivariant maps between Stiefel manifolds.