Vector fields on RP^m x RP^n

TL;DR

This paper investigates the maximum number of linearly independent vector fields on products of real projective spaces, using BP-cohomology to derive new upper bounds that improve upon previous results.

Contribution

It introduces new upper bounds for the span of P^m x P^n using BP-cohomology, advancing understanding of vector fields on product manifolds.

Findings

Derived stronger upper bounds for span(P^m x P^n)

Improved understanding of vector fields on product projective spaces

Contributed to the unresolved question of span equality for products

Abstract

The span of a manifold is its maximum number of linearly independent vector fields. We discuss the question, still unresolved, of whether span(P^m x P^n) always equals span(P^m) + span(P^n). Here P^n denotes real projective space. We use BP-cohomology to obtain new upper bounds for span(P^m x P^n), much stronger than previously known bounds.