\v{C}ech cohomology of infinite projective spaces, flag manifolds, and related spaces

TL;DR

This paper computes the cech cohomology rings of infinite products of projective spaces and flag manifolds, extending methods to a broad class of infinite-dimensional topological spaces.

Contribution

It introduces a method to compute cech cohomology rings for countable products of certain topological spaces, including infinite projective spaces and flag manifolds.

Findings

Computed cech cohomology rings for infinite projective spaces and flag manifolds

Developed a general method for cohomology of countably infinite products of paracompact spaces

Extended cohomology computation techniques to a broad class of infinite-dimensional spaces

Abstract

We compute the \v{C}ech cohomology ring of a countable product of infinite projective spaces, and that of an infinite flag manifold. The method of our first result in fact computes the cohomology ring of a countably infinite product of paracompact Hausdorff spaces, under some mild assumptions.